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ODE |
Solved? |
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\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=6 x+3 y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=10 y \\ y^{\prime }=-10 x \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{2} \\ y^{\prime }=-8 x \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=8 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=6 x-y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=10 x-7 y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=13 x+4 y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-9 x+6 y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} 10 x_{1}^{\prime }=-x_{1}+x_{3} \\ 10 x_{2}^{\prime }=x_{1}-x_{2} \\ 10 x_{3}^{\prime }=x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=-x+3 y \\ y^{\prime }=2 y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+2 y \\ y^{\prime }=-3 x+4 y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=5 x-3 y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-4 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=x+9 y \\ y^{\prime }=-2 x-5 y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=4 x+y+2 t \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+2 y-{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y+2 \sin \left (2 t \right ) \\ y^{\prime }=x-2 y-\cos \left (2 t \right ) \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }+2 y^{\prime }=4 x+5 y \\ 2 x^{\prime }-y^{\prime }=3 x \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} -x^{\prime }+2 y^{\prime }=x+3 y+{\mathrm e}^{t} \\ 3 x^{\prime }-4 y^{\prime }=x-15 y+{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+z \\ y^{\prime }=6 x-y \\ z^{\prime }=-x-2 y-z \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-4 x+4 y-2 z \\ z^{\prime }=-4 y+4 z \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=y+z+{\mathrm e}^{-t} \\ y^{\prime }=x+z \\ z^{\prime }=x+y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=3 x \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }=5 x-y-t^{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=x t -{\mathrm e}^{t} y+\cos \left (t \right ) \\ y^{\prime }={\mathrm e}^{-t} x+t^{2} y-\sin \left (t \right ) \end {array}\right ]
\] |
✗ |
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\[
{}\left [\begin {array}{c} x^{\prime }=y+z \\ y^{\prime }=x+z \\ z^{\prime }=x+y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y \\ y^{\prime }=x+y+2 z \\ z^{\prime }=5 y-7 z \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y+z+t \\ y^{\prime }=x-3 z+t^{2} \\ z^{\prime }=6 y-7 z+t^{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=x t -y+{\mathrm e}^{t} z \\ y^{\prime }=2 x+t^{2} y-z \\ z^{\prime }={\mathrm e}^{-t} x+3 t y+t^{3} z \end {array}\right ]
\] |
✗ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=2 x_{3} \\ x_{3}^{\prime }=3 x_{4} \\ x_{4}^{\prime }=4 x_{1} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3}+1 \\ x_{2}^{\prime }=x_{3}+x_{4}+t \\ x_{3}^{\prime }=x_{1}+x_{4}+t^{2} \\ x_{4}^{\prime }=x_{1}+x_{2}+t^{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-3 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+4 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2} \\ x_{2}^{\prime }=-2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-3 x_{2} \\ x_{2}^{\prime }=6 x_{1}-7 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=-x_{1}+3 x_{2}-2 x_{3} \\ x_{3}^{\prime }=-x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }=6 x_{1}-x_{2} \\ x_{3}^{\prime }=-x_{1}-2 x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}-11 x_{2}-2 x_{3} \\ x_{2}^{\prime }=6 x_{1}+9 x_{2}+2 x_{3} \\ x_{3}^{\prime }=-6 x_{1}-6 x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }=x_{2} \\ x_{3}^{\prime }=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }=-4 x_{2}-x_{4} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+3 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2} \\ x_{2}^{\prime }=6 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+5 x_{2} \\ x_{2}^{\prime }=-6 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=6 x_{1}-5 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=9 x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-9 x_{2} \\ x_{2}^{\prime }=2 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-5 x_{2} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-50 x_{1}+20 x_{2} \\ x_{2}^{\prime }=100 x_{1}-60 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+4 x_{3} \\ x_{2}^{\prime }=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }=2 x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}+7 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+4 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=3 x_{1}+x_{2}+5 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-6 x_{3} \\ x_{2}^{\prime }=2 x_{1}-x_{2}-2 x_{3} \\ x_{3}^{\prime }=4 x_{1}-2 x_{2}-4 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-5 x_{1}-4 x_{2}-2 x_{3} \\ x_{3}^{\prime }=5 x_{1}+5 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=-5 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }=5 x_{1}+5 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }=-4 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }=4 x_{1}+4 x_{2}+2 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+5 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-6 x_{1}-6 x_{2}-5 x_{3} \\ x_{3}^{\prime }=6 x_{1}+6 x_{2}+5 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{3} \\ x_{2}^{\prime }=9 x_{1}-x_{2}+2 x_{3} \\ x_{3}^{\prime }=-9 x_{1}+4 x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+2 x_{2} \\ x_{3}^{\prime }=3 x_{2}+3 x_{3} \\ x_{4}^{\prime }=4 x_{3}+4 x_{4} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+9 x_{4} \\ x_{2}^{\prime }=4 x_{1}+2 x_{2}-10 x_{4} \\ x_{3}^{\prime }=-x_{3}+8 x_{4} \\ x_{4}^{\prime }=x_{4} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }=5 x_{3} \\ x_{4}^{\prime }=-21 x_{3}-2 x_{4} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\ x_{2}^{\prime }=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\ x_{3}^{\prime }=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\ x_{4}^{\prime }=7 x_{1}+x_{2}+x_{3}+4 x_{4} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=3 x \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }=5 x-y-t^{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }=y+z \\ y^{\prime }=x+z \\ z^{\prime }=x+y \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=2 x_{3} \\ x_{3}^{\prime }=3 x_{4} \\ x_{4}^{\prime }=4 x_{1} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3}+1 \\ x_{2}^{\prime }=x_{3}+x_{4}+t \\ x_{3}^{\prime }=x_{1}+x_{4}+t^{2} \\ x_{4}^{\prime }=x_{1}+x_{2}+t^{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=6 x_{1} \\ x_{2}^{\prime }=-3 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+4 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+3 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2} \\ x_{2}^{\prime }=6 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=6 x_{1}-7 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+5 x_{2} \\ x_{2}^{\prime }=-6 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=6 x_{1}-5 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=9 x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-9 x_{2} \\ x_{2}^{\prime }=2 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-5 x_{2} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-50 x_{1}+20 x_{2} \\ x_{2}^{\prime }=100 x_{1}-60 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+4 x_{3} \\ x_{2}^{\prime }=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }=2 x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}+7 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+4 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=x_{1}+7 x_{2}+x_{3} \\ x_{3}^{\prime }=3 x_{1}+x_{2}+5 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-6 x_{3} \\ x_{2}^{\prime }=2 x_{1}-x_{2}-2 x_{3} \\ x_{3}^{\prime }=4 x_{1}-2 x_{2}-4 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-5 x_{1}-4 x_{2}-2 x_{3} \\ x_{3}^{\prime }=5 x_{1}+5 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=-5 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }=5 x_{1}+5 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
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|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }=-4 x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }=4 x_{1}+4 x_{2}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+5 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-6 x_{1}-6 x_{2}-5 x_{3} \\ x_{3}^{\prime }=6 x_{1}+6 x_{2}+5 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{3} \\ x_{2}^{\prime }=9 x_{1}-x_{2}+2 x_{3} \\ x_{3}^{\prime }=-9 x_{1}+4 x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+2 x_{2} \\ x_{3}^{\prime }=3 x_{2}+3 x_{3} \\ x_{4}^{\prime }=4 x_{3}+4 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+9 x_{4} \\ x_{2}^{\prime }=4 x_{1}+2 x_{2}-10 x_{4} \\ x_{3}^{\prime }=-x_{3}+8 x_{4} \\ x_{4}^{\prime }=x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=-21 x_{1}-5 x_{2}-27 x_{3}-9 x_{4} \\ x_{3}^{\prime }=5 x_{3} \\ x_{4}^{\prime }=-21 x_{3}-2 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+x_{3}+7 x_{4} \\ x_{2}^{\prime }=x_{1}+4 x_{2}+10 x_{3}+x_{4} \\ x_{3}^{\prime }=x_{1}+10 x_{2}+4 x_{3}+x_{4} \\ x_{4}^{\prime }=7 x_{1}+x_{2}+x_{3}+4 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-40 x_{1}-12 x_{2}+54 x_{3} \\ x_{2}^{\prime }=35 x_{1}+13 x_{2}-46 x_{3} \\ x_{3}^{\prime }=-25 x_{1}-7 x_{2}+34 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-20 x_{1}+11 x_{2}+13 x_{3} \\ x_{2}^{\prime }=12 x_{1}-x_{2}-7 x_{3} \\ x_{3}^{\prime }=-48 x_{1}+21 x_{2}+31 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=147 x_{1}+23 x_{2}-202 x_{3} \\ x_{2}^{\prime }=-90 x_{1}-9 x_{2}+129 x_{3} \\ x_{3}^{\prime }=90 x_{1}+15 x_{2}-123 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}-7 x_{2}-5 x_{3} \\ x_{2}^{\prime }=-12 x_{1}+7 x_{2}+11 x_{3}+9 x_{4} \\ x_{3}^{\prime }=24 x_{1}-17 x_{2}-19 x_{3}-9 x_{4} \\ x_{4}^{\prime }=-18 x_{1}+13 x_{2}+17 x_{3}+9 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=13 x_{1}-42 x_{2}+106 x_{3}+139 x_{4} \\ x_{2}^{\prime }=2 x_{1}-16 x_{2}+52 x_{3}+70 x_{4} \\ x_{3}^{\prime }=x_{1}+6 x_{2}-20 x_{3}-31 x_{4} \\ x_{4}^{\prime }=-x_{1}-6 x_{2}+22 x_{3}+33 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=23 x_{1}-18 x_{2}-16 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+6 x_{2}+7 x_{3}+9 x_{4} \\ x_{3}^{\prime }=34 x_{1}-27 x_{2}-26 x_{3}-9 x_{4} \\ x_{4}^{\prime }=-26 x_{1}+21 x_{2}+25 x_{3}+12 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=47 x_{1}-8 x_{2}+5 x_{3}-5 x_{4} \\ x_{2}^{\prime }=-10 x_{1}+32 x_{2}+18 x_{3}-2 x_{4} \\ x_{3}^{\prime }=139 x_{1}-40 x_{2}-167 x_{3}-121 x_{4} \\ x_{4}^{\prime }=-232 x_{1}+64 x_{2}+360 x_{3}+248 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=139 x_{1}-14 x_{2}-52 x_{3}-14 x_{4}+28 x_{5} \\ x_{2}^{\prime }=-22 x_{1}+5 x_{2}+7 x_{3}+8 x_{4}-7 x_{5} \\ x_{3}^{\prime }=370 x_{1}-38 x_{2}-139 x_{3}-38 x_{4}+76 x_{5} \\ x_{4}^{\prime }=152 x_{1}-16 x_{2}-59 x_{3}-13 x_{4}+35 x_{5} \\ x_{5}^{\prime }=95 x_{1}-10 x_{2}-38 x_{3}-7 x_{4}+23 x_{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+13 x_{2}-13 x_{6} \\ x_{2}^{\prime }=-14 x_{1}+19 x_{2}-10 x_{3}-20 x_{4}+10 x_{5}+4 x_{6} \\ x_{3}^{\prime }=-30 x_{1}+12 x_{2}-7 x_{3}-30 x_{4}+12 x_{5}+18 x_{6} \\ x_{4}^{\prime }=-12 x_{1}+10 x_{2}-10 x_{3}-9 x_{4}+10 x_{5}+2 x_{6} \\ x_{5}^{\prime }=6 x_{1}+9 x_{2}+6 x_{4}+5 x_{5}-15 x_{6} \\ x_{6}^{\prime }=-14 x_{1}+23 x_{2}-10 x_{3}-20 x_{4}+10 x_{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+4 x_{2} \\ x_{2}^{\prime }=-6 x_{1}-x_{2} \\ x_{3}^{\prime }=6 x_{1}+4 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=3 x_{1}+7 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+2 x_{3} \\ x_{2}^{\prime }=-5 x_{1}-3 x_{2}-7 x_{3} \\ x_{3}^{\prime }=x_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{3} \\ x_{2}^{\prime }=x_{4} \\ x_{3}^{\prime }=-2 x_{1}+2 x_{2}-3 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{1}-2 x_{2}+x_{3}-3 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}-4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}+x_{2} \\ x_{2}^{\prime }=-4 x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+9 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=-7 x_{1}+9 x_{2}+7 x_{3} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=25 x_{1}+12 x_{2} \\ x_{2}^{\prime }=-18 x_{1}-5 x_{2} \\ x_{3}^{\prime }=6 x_{1}+6 x_{2}+13 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-19 x_{1}+12 x_{2}+84 x_{3} \\ x_{2}^{\prime }=5 x_{2} \\ x_{3}^{\prime }=-8 x_{1}+4 x_{2}+33 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-13 x_{1}+40 x_{2}-48 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+23 x_{2}-24 x_{3} \\ x_{3}^{\prime }=3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-4 x_{3} \\ x_{2}^{\prime }=-x_{1}-x_{2}-x_{3} \\ x_{3}^{\prime }=x_{1}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{3} \\ x_{2}^{\prime }=-x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{3} \\ x_{2}^{\prime }=x_{2}-4 x_{3} \\ x_{3}^{\prime }=x_{2}-3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{3} \\ x_{2}^{\prime }=-5 x_{1}-x_{2}-5 x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}+4 x_{2} \\ x_{3}^{\prime }=x_{1}+3 x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2}-3 x_{3} \\ x_{3}^{\prime }=2 x_{1}+3 x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=18 x_{1}+7 x_{2}+4 x_{3} \\ x_{3}^{\prime }=-27 x_{1}-9 x_{2}-5 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+x_{3} \\ x_{3}^{\prime }=-2 x_{1}-4 x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }=x_{2} \\ x_{3}^{\prime }=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }=-4 x_{2}-x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+x_{4} \\ x_{2}^{\prime }=2 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=x_{1}+2 x_{2}+x_{3} \\ x_{4}^{\prime }=x_{2}+x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{2}+7 x_{3} \\ x_{2}^{\prime }=-x_{2}-4 x_{3} \\ x_{3}^{\prime }=x_{2}+3 x_{3} \\ x_{4}^{\prime }=-6 x_{2}-14 x_{3}+x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=39 x_{1}+8 x_{2}-16 x_{3} \\ x_{2}^{\prime }=-36 x_{1}-5 x_{2}+16 x_{3} \\ x_{3}^{\prime }=72 x_{1}+16 x_{2}-29 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=28 x_{1}+50 x_{2}+100 x_{3} \\ x_{2}^{\prime }=15 x_{1}+33 x_{2}+60 x_{3} \\ x_{3}^{\prime }=-15 x_{1}-30 x_{2}-57 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+17 x_{2}+4 x_{3} \\ x_{2}^{\prime }=-x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{2}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+5 x_{2}-5 x_{3} \\ x_{2}^{\prime }=3 x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }=8 x_{1}-8 x_{2}+10 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-15 x_{1}-7 x_{2}+4 x_{3} \\ x_{2}^{\prime }=34 x_{1}+16 x_{2}-11 x_{3} \\ x_{3}^{\prime }=17 x_{1}+7 x_{2}+5 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}+x_{3}-2 x_{4} \\ x_{2}^{\prime }=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4} \\ x_{3}^{\prime }=5 x_{1}-x_{2}+x_{3}+3 x_{4} \\ x_{4}^{\prime }=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}-2 x_{3}+x_{4} \\ x_{2}^{\prime }=3 x_{2}-5 x_{3}+3 x_{4} \\ x_{3}^{\prime }=-13 x_{2}+22 x_{3}-12 x_{4} \\ x_{4}^{\prime }=-27 x_{2}+45 x_{3}-25 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4} \\ x_{2}^{\prime }=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4} \\ x_{3}^{\prime }=-10 x_{1}+3 x_{2}-9 x_{4} \\ x_{4}^{\prime }=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\ x_{2}^{\prime }=3 x_{2} \\ x_{3}^{\prime }=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\ x_{4}^{\prime }=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\ x_{5}^{\prime }=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2}+x_{3} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2}+x_{4} \\ x_{3}^{\prime }=3 x_{3}-4 x_{4} \\ x_{4}^{\prime }=4 x_{3}+3 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-8 x_{3}-3 x_{4} \\ x_{2}^{\prime }=-18 x_{1}-x_{2} \\ x_{3}^{\prime }=-9 x_{1}-3 x_{2}-25 x_{3}-9 x_{4} \\ x_{4}^{\prime }=33 x_{1}+10 x_{2}+90 x_{3}+32 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{10}+\frac {3 x_{2}}{40} \\ x_{2}^{\prime }=\frac {x_{1}}{10}-\frac {x_{2}}{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {9 x_{1}}{5}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=-5 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2} \\ x_{3}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {3 x_{1}}{4}-2 x_{2} \\ x_{2}^{\prime }=x_{1}-\frac {5 x_{2}}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {4 x_{1}}{5}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}+\frac {6 x_{2}}{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }=-\frac {x_{3}}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }=\frac {x_{3}}{10} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}-\frac {x_{2}}{8} \\ x_{2}^{\prime }=2 x_{1}-\frac {x_{2}}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-2 x_{2} \\ x_{2}^{\prime }=8 x_{1}-4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {3 x_{1}}{2}+x_{2} \\ x_{2}^{\prime }=-\frac {x_{1}}{4}-\frac {x_{2}}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {5 x_{1}}{2}+2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{2}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{2}+\frac {x_{2}}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{2}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+9 x_{2} \\ x_{2}^{\prime }=-x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=-4 x_{1}+x_{2} \\ x_{3}^{\prime }=3 x_{1}+6 x_{2}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{2}+x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}-\frac {5 x_{2}}{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}-\frac {5 x_{3}}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}+t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\ x_{2}^{\prime }=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+2 x_{2}+\frac {1}{t} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+\frac {2}{t}+4 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=4 x_{1}+x_{2}-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{4}+\frac {3 x_{2}}{4}+2 t \\ x_{2}^{\prime }=\frac {3 x_{1}}{4}-\frac {5 x_{2}}{4}+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\ x_{2}^{\prime }=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}+\csc \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sec \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}-\frac {x_{2}}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2} \\ x_{2}^{\prime }=2 x_{1}-\frac {x_{2}}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }=x_{1}-2 x_{2}+3 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2} \\ x_{2}^{\prime }=-\frac {5 x_{2}}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=-5 x_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1} \\ x_{2}^{\prime }=-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {9 x_{1}}{5}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-2 \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}-2 \\ x_{2}^{\prime }=x_{1}-2 x_{2}+1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}-1 \\ x_{2}^{\prime }=2 x_{1}-x_{2}+5 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2} \\ y_{2}^{\prime }=2 y_{1}+y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-\frac {5 y_{1}}{4}+\frac {3 y_{2}}{4} \\ y_{2}^{\prime }=\frac {3 y_{1}}{4}-\frac {5 y_{2}}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-\frac {4 y_{1}}{5}+\frac {3 y_{2}}{5} \\ y_{2}^{\prime }=-\frac {2 y_{1}}{5}-\frac {11 y_{2}}{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-4 y_{2} \\ y_{2}^{\prime }=-y_{1}-y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-4 y_{2} \\ y_{2}^{\prime }=-y_{1}-y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-3 y_{2} \\ y_{2}^{\prime }=2 y_{1}-y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{2}^{\prime }=y_{1}-2 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-4 y_{1}+y_{2}-y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-4 y_{2}-8 y_{3} \\ y_{2}^{\prime }=-4 y_{1}-4 y_{3} \\ y_{3}^{\prime }=-8 y_{1}-4 y_{2}-6 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+5 y_{2}+8 y_{3} \\ y_{2}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{3}^{\prime }=-y_{1}-y_{2}-y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-y_{2}+2 y_{3} \\ y_{2}^{\prime }=12 y_{1}-4 y_{2}+10 y_{3} \\ y_{3}^{\prime }=-6 y_{1}+y_{2}-7 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-y_{2}-4 y_{3} \\ y_{2}^{\prime }=4 y_{1}-3 y_{2}-2 y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}-y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}+2 y_{2}-6 y_{3} \\ y_{2}^{\prime }=2 y_{1}+6 y_{2}+2 y_{3} \\ y_{3}^{\prime }=-2 y_{1}-2 y_{2}+2 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-2 y_{1}+7 y_{2}-2 y_{3} \\ y_{3}^{\prime }=-10 y_{1}+10 y_{2}-5 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=3 y_{1}+5 y_{2}+y_{3} \\ y_{3}^{\prime }=-6 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-y_{1}+7 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-y_{1}-11 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+y_{2} \\ y_{2}^{\prime }=-y_{1}+y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}+12 y_{2} \\ y_{2}^{\prime }=-3 y_{1}-8 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-10 y_{1}+9 y_{2} \\ y_{2}^{\prime }=-4 y_{1}+2 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-13 y_{1}+16 y_{2} \\ y_{2}^{\prime }=-9 y_{1}+11 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2}+y_{3} \\ y_{2}^{\prime }=-4 y_{1}+6 y_{2}+y_{3} \\ y_{3}^{\prime }=4 y_{2}+2 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3} \\ y_{2}^{\prime }=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3} \\ y_{3}^{\prime }=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=-2 y_{1}+2 y_{3} \\ y_{3}^{\prime }=-y_{1}+3 y_{2}-y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-2 y_{1}+3 y_{2}-y_{3} \\ y_{3}^{\prime }=2 y_{1}-y_{2}+3 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=6 y_{1}-5 y_{2}+3 y_{3} \\ y_{2}^{\prime }=2 y_{1}-y_{2}+3 y_{3} \\ y_{3}^{\prime }=2 y_{1}+y_{2}+y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-11 y_{1}+8 y_{2} \\ y_{2}^{\prime }=-2 y_{1}-3 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=15 y_{1}-9 y_{2} \\ y_{2}^{\prime }=16 y_{1}-9 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-4 y_{2} \\ y_{2}^{\prime }=y_{1}-7 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+24 y_{2} \\ y_{2}^{\prime }=-6 y_{1}+17 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+3 y_{2} \\ y_{2}^{\prime }=-3 y_{1}-y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{3}^{\prime }=-y_{1}-y_{2}-y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}+2 y_{2}+y_{3} \\ y_{2}^{\prime }=-2 y_{1}+2 y_{2}+y_{3} \\ y_{3}^{\prime }=-3 y_{1}+3 y_{2}+2 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}-4 y_{2}+4 y_{3} \\ y_{2}^{\prime }=y_{1}+y_{3} \\ y_{3}^{\prime }=-9 y_{1}-5 y_{2}+6 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-4 y_{2}-y_{3} \\ y_{2}^{\prime }=3 y_{1}+6 y_{2}+y_{3} \\ y_{3}^{\prime }=-3 y_{1}-2 y_{2}+3 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-8 y_{2}-4 y_{3} \\ y_{2}^{\prime }=-3 y_{1}-y_{2}-4 y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}+9 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-5 y_{1}-y_{2}+11 y_{3} \\ y_{2}^{\prime }=-7 y_{1}+y_{2}+13 y_{3} \\ y_{3}^{\prime }=-4 y_{1}+8 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }=-y_{1}+9 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-2 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+10 y_{2}-12 y_{3} \\ y_{2}^{\prime }=2 y_{1}+2 y_{2}+3 y_{3} \\ y_{3}^{\prime }=2 y_{1}-y_{2}+6 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-4 y_{2}-4 y_{3} \\ y_{2}^{\prime }=2 y_{1}-y_{2}+y_{3} \\ y_{3}^{\prime }=2 y_{1}+3 y_{2}+y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-y_{1}+5 y_{2}-3 y_{3} \\ y_{3}^{\prime }=y_{1}+y_{2}+y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}-12 y_{2}+10 y_{3} \\ y_{2}^{\prime }=2 y_{1}-24 y_{2}+11 y_{3} \\ y_{3}^{\prime }=2 y_{1}-24 y_{2}+8 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-12 y_{2}+8 y_{3} \\ y_{2}^{\prime }=y_{1}-9 y_{2}+4 y_{3} \\ y_{3}^{\prime }=y_{1}-6 y_{2}+y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-4 y_{1}-y_{3} \\ y_{2}^{\prime }=-y_{1}-3 y_{2}-y_{3} \\ y_{3}^{\prime }=y_{1}-2 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-3 y_{2}+4 y_{3} \\ y_{2}^{\prime }=4 y_{1}+5 y_{2}-8 y_{3} \\ y_{3}^{\prime }=2 y_{1}+3 y_{2}-5 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-y_{2} \\ y_{2}^{\prime }=y_{1}-y_{2} \\ y_{3}^{\prime }=-y_{1}-y_{2}-2 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+2 y_{2} \\ y_{2}^{\prime }=-5 y_{1}+5 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-11 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-26 y_{1}+9 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2} \\ y_{2}^{\prime }=-4 y_{1}+5 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-6 y_{2} \\ y_{2}^{\prime }=3 y_{1}-y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-3 y_{2}+y_{3} \\ y_{2}^{\prime }=2 y_{2}+2 y_{3} \\ y_{3}^{\prime }=5 y_{1}+y_{2}+y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}+3 y_{2}+y_{3} \\ y_{2}^{\prime }=y_{1}-5 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-3 y_{1}+7 y_{2}+3 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=y_{2}+y_{3} \\ y_{3}^{\prime }=y_{1}+y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}+y_{2}-3 y_{3} \\ y_{2}^{\prime }=4 y_{1}-y_{2}+2 y_{3} \\ y_{3}^{\prime }=4 y_{1}-2 y_{2}+3 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-3 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y+t \\ y^{\prime }=-4 x+3 y-1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-3 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+{\mathrm e}^{t} \\ y^{\prime }=x-y-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=-2 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=5 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+5 y+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ y^{\prime }=-2 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y+{\mathrm e}^{t} \\ y^{\prime }=x-y+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y+\sin \left (t \right ) \\ y^{\prime }=x-2 y+\tan \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+\textit {f\_1} \left (t \right ) \\ y^{\prime }=-x+f_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=6 x_{1}-3 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2} \\ x_{2}^{\prime }=-4 x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-x_{2}+6 x_{3} \\ x_{2}^{\prime }=-10 x_{1}+4 x_{2}-12 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+6 x_{3} \\ x_{2}^{\prime }=5 x_{2} \\ x_{3}^{\prime }=6 x_{1}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+3 x_{3}+6 x_{4} \\ x_{2}^{\prime }=3 x_{1}+6 x_{2}+9 x_{3}+18 x_{4} \\ x_{3}^{\prime }=5 x_{1}+10 x_{2}+15 x_{3}+30 x_{4} \\ x_{4}^{\prime }=7 x_{1}+14 x_{2}+21 x_{3}+42 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=4 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=-2 x_{1}+2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime }=3 x_{1}+3 x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+10 x_{2}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=-x_{2}-2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}-2 x_{3} \\ x_{2}^{\prime }=-x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \\ x_{3}^{\prime }=x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=3 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=2 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{3} \\ x_{2}^{\prime }=x_{2}-x_{3} \\ x_{3}^{\prime }=-2 x_{1}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2} \\ x_{3}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=-2 x_{1} \\ x_{3}^{\prime }=-3 x_{4} \\ x_{4}^{\prime }=3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=x_{2} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=-2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{3} \\ x_{2}^{\prime }=2 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{3} \\ x_{4}^{\prime }=-x_{3}+2 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}+2 x_{3} \\ x_{2}^{\prime }=-x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-4 x_{2} \\ x_{2}^{\prime }=10 x_{1}+9 x_{2}+x_{3} \\ x_{3}^{\prime }=-4 x_{1}-3 x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=3 x_{3} \\ x_{4}^{\prime }=2 x_{3}+3 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+{\mathrm e}^{c t} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}-x_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\tan \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+f_{1} \left (t \right ) \\ x_{2}^{\prime }=-x_{1}+f_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{2} \\ x_{3}^{\prime }=x_{2}+3 x_{3}+{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}-2 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}+{\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-t^{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+2 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{2}+2 x_{3}+\sin \left (t \right ) \\ x_{2}^{\prime }=-x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}-x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}-3 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+4 x_{3}-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }=-4 x_{2}-x_{3}+t \\ x_{3}^{\prime }=5 x_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2}-4 x_{3}+2 \,{\mathrm e}^{2 t} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-4 x_{3}+{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+x_{3}-{\mathrm e}^{3 t} \\ x_{3}^{\prime }=-3 x_{1}+x_{2}-x_{3}-{\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3}+2 \,{\mathrm e}^{8 t} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3}+{\mathrm e}^{8 t} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3}+2 \,{\mathrm e}^{8 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=-2 x_{1}+2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2}+t \\ x_{2}^{\prime }=2 x_{1}-2 x_{2}+3 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=4 x_{1}+x_{2}-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}-x_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\tan \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+f_{1} \left (t \right ) \\ x_{2}^{\prime }=-x_{1}+f_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2}+1-\operatorname {Heaviside}\left (t -\pi \right ) \\ x_{2}^{\prime }=2 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{2} \\ x_{3}^{\prime }=3 x_{3}+{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}+2 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=3 x_{3} \\ x_{4}^{\prime }=2 x_{3}+3 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{2}-2 x y \\ y^{\prime }=2 y-2 y^{2}-3 x y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-b x y+m \\ y^{\prime }=b x y-g y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x-b x y \\ y^{\prime }=-c y+d x y \\ z^{\prime }=z+x^{2}+y^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-x \,y^{2} \\ y^{\prime }=-y-y \,x^{2} \\ z^{\prime }=1-z+x^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \,y^{2}-x \\ y^{\prime }=x \sin \left (\pi y\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\cos \left (y\right ) \\ y^{\prime }=\sin \left (x\right )-1 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-1-y-{\mathrm e}^{x} \\ y^{\prime }=x^{2}+y \left ({\mathrm e}^{x}-1\right ) \\ z^{\prime }=x+\sin \left (z\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y^{2} \\ y^{\prime }=x^{2}-y \\ z^{\prime }={\mathrm e}^{z}-x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+z-2 \,{\mathrm e}^{-t} \\ y^{\prime }=2 x+y-z-2 \,{\mathrm e}^{-t} \\ z^{\prime }=-3 x+2 y+4 z+3 \,{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-4 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+3 y \\ y^{\prime }=y-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+y-6 z \\ y^{\prime }=10 x-4 y+12 z \\ z^{\prime }=2 x-y+z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+4 z \\ y^{\prime }=2 x+2 z \\ z^{\prime }=4 x+2 y+3 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y+z \\ y^{\prime }=-x-3 y-z \\ z^{\prime }=x+y-z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y+z \\ y^{\prime }=-3 x+2 y+3 z \\ z^{\prime }=x-y-2 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \\ z^{\prime }=2 h \\ h^{\prime }=-2 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y+z \\ y^{\prime }=-2 x+h \\ z^{\prime }=2 h \\ h^{\prime }=-2 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-\frac {\left (x_{1}^{2}+\sqrt {x_{1}^{2}+4 x_{2}^{2}}\right ) x_{1}}{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }=2 x_{1}-x_{2}+5 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{3}-x y \\ y^{\prime }=2 y-y^{5}-y \,x^{4} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2}+1 \\ y^{\prime }=x^{2}-y^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2}-1 \\ y^{\prime }=2 x y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-6 x^{2}-2 x y \\ y^{\prime }=4 y-4 y^{2}-2 x y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\tan \left (x+y\right ) \\ y^{\prime }=x+x^{3} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }={\mathrm e}^{y}-x \\ y^{\prime }={\mathrm e}^{x}+y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}-5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=8 x_{1}-6 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-x_{2} \\ x_{2}^{\prime }=-2 x_{1}+5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-6 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=-8 x_{1}+4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=-5 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{2} \\ x_{2}^{\prime }=-9 x_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x=\cos \left (t \right ) \\ y^{\prime }+y=4 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x=3 t^{2} \\ y^{\prime }+y={\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x=3 t \\ x^{\prime }+2 y^{\prime }+y=\cos \left (2 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y=2 \sin \left (t \right ) \\ x^{\prime }+y^{\prime }=3 y-3 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+3 x-y={\mathrm e}^{t} \\ 5 x-3 y^{\prime }=y+2 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 5 y^{\prime }-3 x^{\prime }-5 y=5 t \\ 3 x^{\prime }-5 y^{\prime }-2 x=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=2 x+3 y \\ z^{\prime }=3 y-2 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-3 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+2 x_{2} \\ x_{2}^{\prime }=x_{2}-x_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+4 x_{2} \\ x_{2}^{\prime }=-4 x_{1}-6 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=-2 x_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=x_{2}-x_{3} \\ x_{3}^{\prime }=x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }=-x_{2}-3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+5 x_{2} \\ x_{2}^{\prime }=-x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}+4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+5 \,{\mathrm e}^{4 t} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+t \\ x_{2}^{\prime }=-2 x_{1}+x_{2}+1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=3 x_{1}-x_{2}+5 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\tan \left (t \right ) x_{1}+3 \cos \left (t \right )^{2} \\ x_{2}^{\prime }=x_{1}+\tan \left (t \right ) x_{2}+2 \sin \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-b x_{1}-a x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{2} \\ x_{2}^{\prime }=-3 x_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+3 x_{2} \\ x_{2}^{\prime }=-2 x_{1}+5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{2}-x_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \\ x_{3}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{t} \\ x_{2}^{\prime }=x_{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{t}+t x_{2} \\ x_{2}^{\prime }=-\frac {x_{1}}{t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-7 x_{2} \\ x_{2}^{\prime }=-x_{1}+4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{2} \\ x_{2}^{\prime }=4 x_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=5 x_{1}-5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+2 x_{2} \\ x_{2}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=5 x_{2}-7 x_{3} \\ x_{3}^{\prime }=2 x_{2}-4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1} \\ x_{2}^{\prime }=x_{1}+5 x_{2}-x_{3} \\ x_{3}^{\prime }=x_{1}+6 x_{2}-2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-x_{1} \\ x_{3}^{\prime }=5 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+3 x_{3} \\ x_{2}^{\prime }=-4 x_{2} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+6 x_{3} \\ x_{2}^{\prime }=-2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=-x_{1}-2 x_{2}-4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{2}+x_{3} \\ x_{2}^{\prime }=-2 x_{1}-x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{3} \\ x_{2}^{\prime }=-3 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+3 x_{3}+4 x_{4} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2}+2 x_{3}+x_{4} \\ x_{3}^{\prime }=4 x_{1}+5 x_{2}+6 x_{3}+7 x_{4} \\ x_{4}^{\prime }=7 x_{1}+6 x_{2}+5 x_{3}+4 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-x_{1} \\ x_{3}^{\prime }=-x_{4} \\ x_{4}^{\prime }=x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+4 x_{2} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-6 x_{2} \\ x_{2}^{\prime }=3 x_{1}+5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \\ x_{3}^{\prime }=2 x_{1}-x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{2} \\ x_{2}^{\prime }=-4 x_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=-b x_{1}-a x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+3 x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1} \\ x_{2}^{\prime }=x_{1}-3 x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=15 x_{1}-32 x_{2}+12 x_{3} \\ x_{2}^{\prime }=8 x_{1}-17 x_{2}+6 x_{3} \\ x_{3}^{\prime }=-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1} \\ x_{2}^{\prime }=x_{1}+4 x_{2} \\ x_{3}^{\prime }=x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=3 x_{2}+2 x_{3} \\ x_{3}^{\prime }=2 x_{1}-2 x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}+5 x_{2} \\ x_{3}^{\prime }=4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}-x_{1} \\ x_{2}^{\prime }=-2 x_{1}-3 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}-2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=x_{1} \\ x_{3}^{\prime }=x_{1}+2 x_{3}+x_{4} \\ x_{4}^{\prime }=x_{2}+2 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+3 x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \\ x_{3}^{\prime }=x_{1}+x_{3}+x_{4} \\ x_{4}^{\prime }=x_{2}+x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=x_{1} \\ x_{3}^{\prime }=x_{1}-x_{4} \\ x_{4}^{\prime }=x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=-x_{1}-3 x_{2}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-3 x_{2}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=-x_{1}+2 x_{2}+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}+t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }=3 x_{2}+{\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}+20 \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }=3 x_{1}+x_{2}+12 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+2 x_{2}+54 t \,{\mathrm e}^{3 t} \\ x_{2}^{\prime }=-2 x_{1}+4 x_{2}+9 \,{\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+4 x_{2}+8 \sin \left (2 t \right ) \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2}+8 \cos \left (2 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}-3 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=-2 x_{1}-x_{2}+6 t \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-{\mathrm e}^{t} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2}+2 x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }=x_{1}-2 x_{2}+2 x_{3}+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-2 x_{2}+2 x_{3}-{\mathrm e}^{3 t} \\ x_{2}^{\prime }=2 x_{1}+4 x_{2}-x_{3}+4 \,{\mathrm e}^{3 t} \\ x_{3}^{\prime }=3 x_{3}+3 \,{\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-3 x_{2}+34 \sin \left (t \right ) \\ x_{2}^{\prime }=-4 x_{1}-2 x_{2}+17 \cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1} \\ x_{2}^{\prime }=3 x_{2}-x_{3} \\ x_{3}^{\prime }=x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=x_{2}-8 x_{3} \\ x_{3}^{\prime }=2 x_{2}-7 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+3 x_{3} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2}-2 x_{3} \\ x_{3}^{\prime }=2 x_{2}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}+6 x_{2}-3 x_{3} \\ x_{2}^{\prime }=-12 x_{1}+10 x_{2}-3 x_{3} \\ x_{3}^{\prime }=-2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=6 x_{2}-7 x_{3}+3 x_{4} \\ x_{3}^{\prime }=3 x_{3}-x_{4} \\ x_{4}^{\prime }=-4 x_{2}+9 x_{3}-3 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2} \\ x_{2}^{\prime }=x_{1} \\ x_{3}^{\prime }=x_{2}-x_{4} \\ x_{4}^{\prime }=x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\left (-1+2 t \right ) x_{1} \\ x_{2}^{\prime }={\mathrm e}^{-t^{2}+t} x_{1}+x_{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=t \cot \left (t^{2}\right ) x_{1}+\frac {t \cos \left (t^{2}\right ) x_{3}}{2} \\ x_{2}^{\prime }=\frac {x_{2}}{t}-x_{3}+2-t \sin \left (t \right ) \\ x_{3}^{\prime }=\csc \left (t^{2}\right ) x_{1}+x_{2}-x_{3}+1-t \cos \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-6 x_{1}+x_{2} \\ x_{2}^{\prime }=6 x_{1}-5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}-2 x_{2} \\ x_{2}^{\prime }=5 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}+5 x_{2} \\ x_{2}^{\prime }=-5 x_{1}+2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+4 x_{3} \\ x_{2}^{\prime }=2 x_{2} \\ x_{3}^{\prime }=-4 x_{1}-5 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \\ x_{3}^{\prime }=6 x_{1}+6 x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+13 x_{2} \\ x_{2}^{\prime }=-x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-10 x_{2} \\ x_{2}^{\prime }=5 x_{1}+11 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-5 x_{2}+x_{3} \\ x_{2}^{\prime }=4 x_{1}-9 x_{2}-x_{3} \\ x_{3}^{\prime }=3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1} \\ x_{2}^{\prime }=2 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }=5 x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-2 x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}-4 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+2 x_{2}-3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}+3 x_{3} \\ x_{2}^{\prime }=-9 x_{1}-3 x_{2}-9 x_{3} \\ x_{3}^{\prime }=4 x_{1}+4 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-17 x_{1}-42 x_{3} \\ x_{2}^{\prime }=-7 x_{1}+4 x_{2}-14 x_{3} \\ x_{3}^{\prime }=7 x_{1}+18 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-16 x_{1}+30 x_{2}-18 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+8 x_{2}+16 x_{3} \\ x_{3}^{\prime }=8 x_{1}-15 x_{2}+9 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}-6 x_{2}-7 x_{3} \\ x_{2}^{\prime }=-3 x_{1}-3 x_{2}-3 x_{3} \\ x_{3}^{\prime }=7 x_{1}+6 x_{2}+7 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2}-2 x_{3} \\ x_{2}^{\prime }=x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+6 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2}-2 x_{3} \\ x_{2}^{\prime }=-4 x_{1}-5 x_{2}-6 x_{3} \\ x_{3}^{\prime }=4 x_{1}+8 x_{2}+7 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-2 x_{2}+2 x_{3} \\ x_{2}^{\prime }=4 x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-x_{2}-2 x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{3} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=x_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+13 x_{2} \\ x_{2}^{\prime }=-x_{1}-2 x_{2} \\ x_{3}^{\prime }=2 x_{3}+4 x_{4} \\ x_{4}^{\prime }=2 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-x_{4} \\ x_{2}^{\prime }=6 x_{2} \\ x_{3}^{\prime }=-x_{3} \\ x_{4}^{\prime }=2 x_{1}+5 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-6 x_{1}+x_{2}+1 \\ x_{2}^{\prime }=6 x_{1}-5 x_{2}+{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}-2 x_{2}+9 t \\ x_{2}^{\prime }=5 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=10 x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+2 x_{2}+\frac {{\mathrm e}^{6 t}}{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}+3 x_{3}+{\mathrm e}^{6 t} \\ x_{2}^{\prime }=-9 x_{1}-3 x_{2}-9 x_{3}+1 \\ x_{3}^{\prime }=4 x_{1}+4 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-2 x_{2}+x_{3}+t \\ x_{2}^{\prime }=x_{1}-4 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+2 x_{2}-3 x_{3}+1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=8 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-6 x_{2} \\ x_{2}^{\prime }=x_{1}-5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+9 x_{2} \\ x_{2}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1} \\ x_{2}^{\prime }=-4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-2 x_{2} \\ x_{2}^{\prime }=x_{1}+4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-7 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=10 x_{1}-8 x_{2} \\ x_{2}^{\prime }=2 x_{1}+2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=3 y_{2}-2 y_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2} \\ y_{2}^{\prime }=3 y_{2}-y_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-y_{2} \\ y_{2}^{\prime }=2 y_{1}+3 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{2} \\ y_{2}^{\prime }=4 y_{2}-y_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}-y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=y_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}-y_{1} \\ y_{2}^{\prime }=3 y_{1}-4 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 y_{1}^{\prime }=y_{1}+y_{2} \\ 2 y_{2}^{\prime }=5 y_{2}-3 y_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{2} \\ y_{2}^{\prime }=y_{1}+2 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=1 \\ y_{2}^{\prime }=2 y_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 y_{1}^{\prime }+y_{2}^{\prime }-4 y_{1}-y_{2}={\mathrm e}^{x} \\ y_{1}^{\prime }+3 y_{1}+y_{2}=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=-y_{1}+y_{3} \\ y_{3}^{\prime }=-y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x-y=0 \\ x+y^{\prime }-2 y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+x-5 y^{\prime }-4 y=0 \\ -y^{\prime }-2 x+y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+3 y=0 \\ 3 x-y^{\prime }+y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y=0 \\ x^{\prime }+x-y^{\prime }=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }-3 x-4 y=0 \\ x+y^{\prime \prime }+y=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }-y_{2}=0 \\ 4 y_{1}+y_{2}^{\prime }-4 y_{2}-2 y_{3}=0 \\ -2 y_{1}+y_{2}+y_{3}^{\prime }+y_{3}=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }-2 y_{1}+3 y_{2}-3 y_{3}=0 \\ -4 y_{1}+y_{2}^{\prime }+5 y_{2}-3 y_{3}=0 \\ -4 y_{1}+4 y_{2}+y_{3}^{\prime }-2 y_{3}=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x+2 y=8 \\ 2 x+y^{\prime }-2 y=2 \,{\mathrm e}^{-t}-8 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y+t \,{\mathrm e}^{-t} \\ y^{\prime }=2 x-3 y+{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x-2 y={\mathrm e}^{t} \\ -4 x+y^{\prime }-3 y=1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-4 x+3 y=\sin \left (t \right ) \\ -2 x+y^{\prime }+y=-2 \cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y=0 \\ -x+y^{\prime }={\mathrm e}^{t}+{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x+5 y=0 \\ -x+y^{\prime }-2 y=\sin \left (2 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-2 x+2 y^{\prime }=-4 \,{\mathrm e}^{2 t} \\ 2 x^{\prime }-3 x+3 y^{\prime }-y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+2 x+y^{\prime }-6 y=5 \,{\mathrm e}^{t} \\ 4 x^{\prime }+2 x+y^{\prime }-8 y=5 \,{\mathrm e}^{t}+2 t -3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-5 x+3 y=2 \,{\mathrm e}^{3 t} \\ -x+y^{\prime }-y=5 \,{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-2 x+y=0 \\ x+y^{\prime }-2 y=-5 \,{\mathrm e}^{t} \sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+4 x+2 y=\frac {2}{{\mathrm e}^{t}-1} \\ 6 x-y^{\prime }+3 y=\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y=\sec \left (t \right ) \\ -2 x+y^{\prime }+y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x-2 y=16 t \,{\mathrm e}^{t} \\ 2 x-y^{\prime }-2 y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-2 x+y=5 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x+y^{\prime }-2 y=10 \,{\mathrm e}^{t} \sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-4 x+3 y=\sin \left (t \right ) \\ 2 x+y^{\prime }-y=2 \cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-2 x-y=2 \,{\mathrm e}^{t} \\ x-y^{\prime }+2 y=3 \,{\mathrm e}^{4 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y=40 \,{\mathrm e}^{3 t} \\ x^{\prime }+x-y^{\prime }=36 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-2 x-y=2 \,{\mathrm e}^{t} \\ y^{\prime }-2 y-4 z=4 \,{\mathrm e}^{2 t} \\ x-z^{\prime }-z=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+2 x-2 y^{\prime }=0 \\ 3 x^{\prime }+y^{\prime \prime }-8 y=240 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x-2 y=0 \\ x-y^{\prime }=15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y=2 \sin \left (t \right ) \left (1-\operatorname {Heaviside}\left (t -\pi \right )\right ) \\ 2 x-y^{\prime }-y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+x-5 y^{\prime }-4 y=28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right ) \\ 3 x^{\prime }-2 x-4 y^{\prime }+y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=-4 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+3 x_{2} \\ x_{2}^{\prime }=-3 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}-x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{1}+2 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2}-x_{3} \\ x_{2}^{\prime }=3 x_{1}-4 x_{2}-3 x_{3} \\ x_{3}^{\prime }=2 x_{1}-4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-2 x_{2}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}-2 x_{3} \\ x_{2}^{\prime }=4 x_{1}+x_{2} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+26 \sin \left (t \right ) \\ x_{2}^{\prime }=3 x_{1}+4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+8 x_{2}+9 t \\ x_{2}^{\prime }=x_{1}+x_{2}+3 \,{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+2 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+4 x_{2}+\frac {{\mathrm e}^{3 t}}{1+{\mathrm e}^{2 t}} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-2 x_{2}+\frac {2}{{\mathrm e}^{t}-1} \\ x_{2}^{\prime }=6 x_{1}+3 x_{2}-\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=-2 x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}+x_{2}+\frac {4}{\sin \left (2 t \right )} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+27 t \\ x_{2}^{\prime }=-x_{1}+4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+35 \,{\mathrm e}^{t} t^{{3}/{2}} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}-x_{3}+6 \,{\mathrm e}^{-t} \\ x_{3}^{\prime }=2 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2}-x_{3} \\ x_{2}^{\prime }=-x_{1}+x_{2}+x_{3}+12 t \\ x_{3}^{\prime }=x_{1}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2}-2 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2} \\ x_{3}^{\prime }=6 x_{1}-6 x_{2}+5 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-x_{3}+4 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2} \\ x_{3}^{\prime }=3 x_{1}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+2 x_{3} \\ x_{2}^{\prime }=x_{1}+2 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}-x_{3}+4 \sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }=x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}-x_{3}+2 \,{\mathrm e}^{2 t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}-3 x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}+2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{3}+24 t \\ x_{2}^{\prime }=x_{1}-x_{2} \\ x_{3}^{\prime }=3 x_{1}-x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y^{\prime }+y=-{\mathrm e}^{t} \\ x+y^{\prime }-y={\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x+y^{\prime }+y=t \\ 5 x+y^{\prime }+3 y=t^{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x+2 y^{\prime }+7 y={\mathrm e}^{t}+2 \\ -2 x+y^{\prime }+3 y={\mathrm e}^{t}-1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y^{\prime }+3 y={\mathrm e}^{-t}-1 \\ x^{\prime }+2 x+y^{\prime }+3 y=1+{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+y^{\prime }+2 y=1+{\mathrm e}^{t} \\ y^{\prime }+2 y+z^{\prime }+z={\mathrm e}^{t}+2 \\ x^{\prime }-x+z^{\prime }+z=3+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }=2 x_{1}-9 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{2} \\ x_{2}^{\prime }=5 x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+3 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}+2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }=x_{1}-2 x_{2}+3 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=16 x_{1}-5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=3 x_{1}-4 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }=2 x_{1}-9 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+3 x_{2} \\ x_{2}^{\prime }=-3 x_{1}+5 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-18 x_{2} \\ x_{2}^{\prime }=2 x_{1}-9 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-8 \\ x_{2}^{\prime }=x_{1}+x_{2}+3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-8 \\ x_{2}^{\prime }=x_{1}+x_{2}+3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1} \\ y_{2}^{\prime }=y_{1}+y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=6 y_{1}+y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}+y_{2}+{\mathrm e}^{3 x} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+x y_{3} \\ y_{2}^{\prime }=y_{2}+x^{3} y_{3} \\ y_{3}^{\prime }=2 x y_{1}-y_{2}+{\mathrm e}^{x} y_{3} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+t -1 \\ y^{\prime }=3 x+2 y-5 t -2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=y-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+6 y \\ y^{\prime }=2 x+6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-5 t +2 \\ y^{\prime }=4 x-2 y-8 t -8 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+\sqrt {2}\, y \\ y^{\prime }=\sqrt {2}\, x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+3 y \\ y^{\prime }=-6 x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-5 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=-4 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+z \\ y^{\prime }=-2 x-y+3 z \\ z^{\prime }=x+y+z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y-z \\ y^{\prime }=2 x-y-4 z \\ z^{\prime }=3 x-y+z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y-4 t +1 \\ y^{\prime }=-x+2 y+3 t +4 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y-t +3 \\ y^{\prime }=x+4 y+t -2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y-t +3 \\ y^{\prime }=-x-5 y+t +1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x y+1 \\ y^{\prime }=y-x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=t y+1 \\ y^{\prime }=-x t +y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-5 y \\ y^{\prime }=4 x+8 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-7 y \\ y^{\prime }=5 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y-9 z \\ y^{\prime }=6 x-y \\ z^{\prime }=10 x+4 y+3 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+2 z \\ z^{\prime }=z-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y+z+t -1 \\ y^{\prime }=2 x+y-z-3 t^{2} \\ z^{\prime }=x+y+z+t^{2}-t +2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y+{\mathrm e}^{-t} \sin \left (2 t \right ) \\ y^{\prime }=5 x+9 z+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\ z^{\prime }=y+6 z-{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y+{\mathrm e}^{t} \\ y^{\prime }=-x+3 y-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\ y^{\prime }=4 x+y+z+2 \,{\mathrm e}^{5 t} \\ z^{\prime }=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y+2 z+{\mathrm e}^{-t}-3 t \\ y^{\prime }=3 x-4 y+z+2 \,{\mathrm e}^{-t}+t \\ z^{\prime }=-2 x+5 y+6 z+2 \,{\mathrm e}^{-t}-t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-7 y+4 \sin \left (t \right )+\left (-4+t \right ) {\mathrm e}^{4 t} \\ y^{\prime }=x+y+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+5 y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+\frac {y}{4} \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+z \\ y^{\prime }=6 x-y \\ z^{\prime }=-x-2 y-z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+z \\ y^{\prime }=x+y \\ z^{\prime }=-2 x-z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=4 x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+2 y \\ y^{\prime }=-\frac {5 x}{2}+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {5 x}{2}+2 y \\ y^{\prime }=\frac {3 x}{4}-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=10 x-5 y \\ y^{\prime }=8 x-12 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 x+2 y \\ y^{\prime }=-3 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=2 y \\ z^{\prime }=y-z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-7 y \\ y^{\prime }=5 x+10 y+4 z \\ z^{\prime }=5 y+2 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=x+2 y+z \\ z^{\prime }=3 y-z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+z \\ y^{\prime }=y \\ z^{\prime }=x+z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-y \\ y^{\prime }=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-y \\ y^{\prime }=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+4 y+2 z \\ y^{\prime }=4 x-y-2 z \\ z^{\prime }=6 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {x}{2} \\ y^{\prime }=x-\frac {y}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+4 z \\ y^{\prime }=2 y \\ z^{\prime }=x+y+z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\ y^{\prime }=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\ z^{\prime }=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\ x_{2}^{\prime }=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\ x_{3}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{4}^{\prime }=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\ x_{5}^{\prime }=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=9 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 x+5 y \\ y^{\prime }=-5 x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+3 y \\ y^{\prime }=-3 x+5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=12 x-9 y \\ y^{\prime }=4 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y-z \\ y^{\prime }=x+y-z \\ z^{\prime }=x-y+z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+4 z \\ y^{\prime }=2 x+2 z \\ z^{\prime }=4 x+2 y+3 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+2 z \\ z^{\prime }=2 y+5 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=3 y+z \\ z^{\prime }=z-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x+2 y-z \\ z^{\prime }=y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+y \\ y^{\prime }=4 y+z \\ z^{\prime }=4 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y \\ y^{\prime }=-x+6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z \\ y^{\prime }=y \\ z^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+5 y \\ y^{\prime }=-2 x+6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y \\ y^{\prime }=5 x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-8 y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z \\ y^{\prime }=-z \\ z^{\prime }=y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y+2 z \\ y^{\prime }=3 x+6 z \\ z^{\prime }=-4 x-3 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-12 y-14 z \\ y^{\prime }=x+2 y-3 z \\ z^{\prime }=x+y-2 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y-7 \\ y^{\prime }=-x-2 y+5 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+9 y+2 \\ y^{\prime }=-x+11 y+6 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-2 x+5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+4 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-x+2 y+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-7 y+10 \\ y^{\prime }=x-2 y-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 x+4 y \\ y^{\prime }=-6 x-y \\ z^{\prime }=6 x+4 y+3 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=3 x+7 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x+5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+y \\ y^{\prime }=-4 x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \\ z^{\prime }=z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-z \\ y^{\prime }=-x+2 z \\ z^{\prime }=-x-2 y+4 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+2 t +1 \\ y^{\prime }=5 x+y+3 t -1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=t +y \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x=t +y \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=y+t +\sin \left (t \right )+\cos \left (t \right ) \\ x^{\prime }+y^{\prime }=2 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x \\ y^{\prime }=b \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a y \\ y^{\prime }=-a x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a y \\ y^{\prime }=b x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x-y \\ y^{\prime }=x+a y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+b y \\ y^{\prime }=c x+b y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} a x^{\prime }+b y^{\prime }=\alpha x+\beta y \\ b x^{\prime }-a y^{\prime }=\beta x-\alpha y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=2 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+3 x+4 y=0 \\ y^{\prime }+2 x+5 y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x-2 y \\ y^{\prime }=x-7 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a_{1} x+b_{1} y+c_{1} \\ y^{\prime }=a_{2} x+b_{2} y+c_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 y=3 t \\ y^{\prime }-2 x=4 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y-t^{2}+6 t +1=0 \\ -x+y^{\prime }=-3 t^{2}+3 t +1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+3 x-y={\mathrm e}^{2 t} \\ y^{\prime }+x+5 y={\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x+y^{\prime }+y={\mathrm e}^{2 t}+t \\ x^{\prime }-x+y^{\prime }+3 y={\mathrm e}^{t}-1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-y={\mathrm e}^{t} \\ 2 x^{\prime }+y^{\prime }+2 y=\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }+9 y^{\prime }+2 x+31 y={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+x+24 y=3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }+9 y^{\prime }+11 x+31 y={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+8 x+24 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }+9 y^{\prime }+44 x+49 y=t \\ 3 x^{\prime }+7 y^{\prime }+34 x+38 y={\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x f \left (t \right )+y g \left (t \right ) \\ y^{\prime }=-x g \left (t \right )+y f \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+\left (a x+b y\right ) f \left (t \right )=g \left (t \right ) \\ y^{\prime }+\left (c x+d y\right ) f \left (t \right )=h \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \cos \left (t \right ) \\ y^{\prime }=x \,{\mathrm e}^{-\sin \left (t \right )} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+y=0 \\ t y^{\prime }+x=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+2 x=t \\ t y^{\prime }-\left (t +2\right ) x-t y=-t \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+2 x-2 y=t \\ t y^{\prime }+x+5 y=t^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t^{2} \left (1-\sin \left (t \right )\right ) x^{\prime }=t \left (1-2 \sin \left (t \right )\right ) x+t^{2} y \\ t^{2} \left (1-\sin \left (t \right )\right ) y^{\prime }=\left (t \cos \left (t \right )-\sin \left (t \right )\right ) x+t \left (1-t \cos \left (t \right )\right ) y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }+y=f \left (t \right ) \\ x^{\prime \prime }+y^{\prime \prime }+y^{\prime }+x+y=g \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-3 x=0 \\ x^{\prime \prime }+y^{\prime }-2 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x-y^{\prime }=2 t \\ x^{\prime \prime }+y^{\prime }-9 x+3 y=\sin \left (2 t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+2 y=0 \\ x^{\prime \prime }-2 y^{\prime }=2 t -\cos \left (2 t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }-t y^{\prime }-2 y=0 \\ t x^{\prime \prime }+2 x^{\prime }+x t =0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+a y=0 \\ y^{\prime \prime }-a^{2} y=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=a x+b y \\ y^{\prime \prime }=c x+d y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=a_{1} x+b_{1} y+c_{1} \\ y^{\prime \prime }=a_{2} x+b_{2} y+c_{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+x+y=-5 \\ y^{\prime \prime }-4 x-3 y=-3 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=\left (3 \cos \left (a t +b \right )^{2}-1\right ) c^{2} x+\frac {3 c^{2} y \sin \left (2 a t b \right )}{2} \\ y^{\prime \prime }=\left (3 \sin \left (a t +b \right )^{2}-1\right ) c^{2} y+\frac {3 c^{2} x \sin \left (2 a t b \right )}{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+6 x+7 y=0 \\ y^{\prime \prime }+3 x+2 y=2 t \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }-a y^{\prime }+b x=0 \\ y^{\prime \prime }+a x^{\prime }+b y=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} a_{1} x^{\prime \prime }+b_{1} x^{\prime }+c_{1} x-A y^{\prime }=B \,{\mathrm e}^{i \omega t} \\ a_{2} y^{\prime \prime }+b_{2} y^{\prime }+c_{2} y+A x^{\prime }=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+a \left (x^{\prime }-y^{\prime }\right )+b_{1} x=c_{1} {\mathrm e}^{i \omega t} \\ y^{\prime \prime }+a \left (y^{\prime }-x^{\prime }\right )+b_{2} y=c_{2} {\mathrm e}^{i \omega t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} \operatorname {a11} x^{\prime \prime }+\operatorname {b11} x^{\prime }+\operatorname {c11} x+\operatorname {a12} y^{\prime \prime }+\operatorname {b12} y^{\prime }+\operatorname {c12} y=0 \\ \operatorname {a21} x^{\prime \prime }+\operatorname {b21} x^{\prime }+\operatorname {c21} x+\operatorname {a22} y^{\prime \prime }+\operatorname {b22} y^{\prime }+\operatorname {c22} y=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }-2 x^{\prime }-y^{\prime }+y=0 \\ y^{\prime \prime \prime }-y^{\prime \prime }+2 x^{\prime }-x=t \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+y^{\prime \prime }+y^{\prime }=\sinh \left (2 t \right ) \\ 2 x^{\prime \prime }+y^{\prime \prime }=2 t \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }-x^{\prime }+y^{\prime }=0 \\ x^{\prime \prime }+y^{\prime \prime }-x=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 x-2 y \\ z^{\prime }=2 y+3 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x \\ y^{\prime }=x-2 y \\ z^{\prime }=x-4 y+z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-z \\ y^{\prime }=x+y \\ z^{\prime }=x+z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y+z=0 \\ -x+y^{\prime }-y=t \\ z^{\prime }-x-z=t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} a x^{\prime }=b c \left (y-z\right ) \\ b y^{\prime }=c a \left (z-x\right ) \\ c z^{\prime }=a b \left (x-y\right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=c y-b z \\ y^{\prime }=a z-c x \\ z^{\prime }=b x-a y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=h \left (t \right ) y-g \left (t \right ) z \\ y^{\prime }=f \left (t \right ) z-h \left (t \right ) x \\ z^{\prime }=x g \left (t \right )-y f \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=y+z-x \\ z^{\prime }=x-y+z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+48 y-28 z \\ y^{\prime }=-4 x+40 y-22 z \\ z^{\prime }=-6 x+57 y-31 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-72 y+44 z \\ y^{\prime }=4 x-4 y+26 z \\ z^{\prime }=6 x-63 y+38 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+g y+\beta z \\ y^{\prime }=g x+b y+\alpha z \\ z^{\prime }=\beta x+\alpha y+c z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }=2 x-t \\ t^{3} y^{\prime }=-x+t^{2} y+t \\ t^{4} z^{\prime }=-x-t^{2} y+t^{3} z+t \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} a t x^{\prime }=b c \left (y-z\right ) \\ b t y^{\prime }=c a \left (z-x\right ) \\ c t z^{\prime }=a b \left (x-y\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=a x_{2}+b x_{3} \cos \left (c t \right )+b x_{4} \sin \left (c t \right ) \\ x_{2}^{\prime }=-a x_{1}+b x_{3} \sin \left (c t \right )-b x_{4} \cos \left (c t \right ) \\ x_{3}^{\prime }=-b x_{1} \cos \left (c t \right )-b x_{2} \sin \left (c t \right )+a x_{4} \\ x_{4}^{\prime }=-b x_{1} \sin \left (c t \right )+b x_{2} \cos \left (c t \right )-a x_{3} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \left (x+y\right ) \\ y^{\prime }=y \left (x+y\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\left (a y+b \right ) x \\ y^{\prime }=\left (c x+d \right ) y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (a \left (p x+q y\right )+\alpha \right ) \\ y^{\prime }=y \left (\beta +b \left (p x+q y\right )\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=h \left (a -x\right ) \left (c -x-y\right ) \\ y^{\prime }=k \left (b -y\right ) \left (c -x-y\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y^{2}-\cos \left (x\right ) \\ y^{\prime }=-y \sin \left (x\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \,y^{2}+x+y \\ y^{\prime }=y \,x^{2}-x-y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-x \left (x^{2}+y^{2}\right ) \\ y^{\prime }=-x+y-y \left (x^{2}+y^{2}\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y+x \left (x^{2}+y^{2}-1\right ) \\ y^{\prime }=x+y \left (x^{2}+y^{2}-1\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \left (x^{2}+y^{2}\right ) \\ y^{\prime }=\left \{\begin {array}{cc} x^{2}+y^{2} & 2 x\le x^{2}+y^{2} \\ \left (\frac {x}{2}-\frac {y^{2}}{2 x}\right ) \left (x^{2}+y^{2}\right ) & \operatorname {otherwise} \end {array}\right . \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y+\left (\left \{\begin {array}{cc} x \left (x^{2}+y^{2}-1\right ) \sin \left (\frac {1}{x^{2}+y^{2}}\right ) & x^{2}+y^{2}\neq 1 \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \\ y^{\prime }=x+\left (\left \{\begin {array}{cc} y \left (x^{2}+y^{2}-1\right ) \sin \left (\frac {1}{x^{2}+y^{2}}\right ) & x^{2}+y^{2}\neq 1 \\ 0 & \operatorname {otherwise} \end {array}\right .\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} \left (t^{2}+1\right ) x^{\prime }=-x t +y \\ \left (t^{2}+1\right ) y^{\prime }=-x-t y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} \left (x^{2}+y^{2}-t^{2}\right ) x^{\prime }=-2 x t \\ \left (x^{2}+y^{2}-t^{2}\right ) y^{\prime }=-2 t y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} {x^{\prime }}^{2}+t x^{\prime }+a y^{\prime }-x=0 \\ x^{\prime } y^{\prime }+t y^{\prime }-y=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x=t x^{\prime }+f \left (x^{\prime }, y^{\prime }\right ) \\ y=t y^{\prime }+g \left (x^{\prime }, y^{\prime }\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=a \,{\mathrm e}^{2 x}-{\mathrm e}^{-x}+{\mathrm e}^{-2 x} \cos \left (y\right )^{2} \\ y^{\prime \prime }={\mathrm e}^{-2 x} \sin \left (y\right ) \cos \left (y\right )-\frac {\sin \left (y\right )}{\cos \left (y\right )^{3}} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=\frac {k x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \\ y^{\prime \prime }=\frac {k y}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-z \\ y^{\prime }=x^{2}+y \\ z^{\prime }=x^{2}+z \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} a x^{\prime }=\left (b -c \right ) y z \\ b y^{\prime }=\left (c -a \right ) z x \\ c z^{\prime }=\left (a -b \right ) x y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (y-z\right ) \\ y^{\prime }=y \left (z-x\right ) \\ z^{\prime }=z \left (x-y\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }=x y \\ y^{\prime }+z^{\prime }=y z \\ x^{\prime }+z^{\prime }=x z \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {x^{2}}{2}-\frac {y}{24} \\ y^{\prime }=2 x y-3 z \\ z^{\prime }=3 x z-\frac {y^{2}}{6} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (y^{2}-z^{2}\right ) \\ y^{\prime }=y \left (z^{2}-x^{2}\right ) \\ z^{\prime }=z \left (x^{2}-y^{2}\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (y^{2}-z^{2}\right ) \\ y^{\prime }=-y \left (z^{2}+x^{2}\right ) \\ z^{\prime }=z \left (x^{2}+y^{2}\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \,y^{2}+x+y \\ y^{\prime }=y \,x^{2}-x-y \\ z^{\prime }=y^{2}-x^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} \left (x-y\right ) \left (x-z\right ) x^{\prime }=f \left (t \right ) \\ \left (y-x\right ) \left (y-z\right ) y^{\prime }=f \left (t \right ) \\ \left (z-x\right ) \left (z-y\right ) z^{\prime }=f \left (t \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime } \sin \left (x_{2}\right )=x_{4} \sin \left (x_{3}\right )+x_{5} \cos \left (x_{3}\right ) \\ x_{2}^{\prime }=x_{4} \cos \left (x_{3}\right )-x_{5} \sin \left (x_{3}\right ) \\ x_{3}^{\prime }+x_{1}^{\prime } \cos \left (x_{2}\right )=a \\ x_{4}^{\prime }-\left (1-\lambda \right ) a x_{5}=-m \sin \left (x_{2}\right ) \cos \left (x_{3}\right ) \\ x_{5}^{\prime }+\left (1-\lambda \right ) a x_{4}=m \sin \left (x_{2}\right ) \sin \left (x_{3}\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+3 x+2 y={\mathrm e}^{t} \\ 4 x-3 y^{\prime }+3 y=3 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=-4 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-3 y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 y \\ y^{\prime }=6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y \\ y^{\prime }=-x-14 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 y-3 x \\ y^{\prime }=x+2 y-1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=3 y-3 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=6 x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+3 y \\ y^{\prime }=2 x-10 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 y \\ y^{\prime }=-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y+1 \\ y^{\prime }=x+y+2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+3 y+{\mathrm e}^{-t} \\ y^{\prime }=2 x-10 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\cos \left (w t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+3 \\ y^{\prime }=7 x+5 y+2 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=3 x+7 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-2 x-4 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-y={\mathrm e}^{4 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=-2 t \\ x^{\prime }+y^{\prime }-3 x-y=t^{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+x={\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-2 y=2 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-3 x-4 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y={\mathrm e}^{-t} \\ x^{\prime }+2 x+y^{\prime }+y={\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-3 x-y=t \\ x^{\prime }+y^{\prime }-4 x-y={\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-6 y={\mathrm e}^{3 t} \\ x^{\prime }+2 y^{\prime }-2 x-6 y=t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y=3 t \\ x^{\prime }+2 y^{\prime }-2 x-3 y=1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }+2 y=\sin \left (t \right ) \\ x^{\prime }+y^{\prime }-x-y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y^{\prime }-2 x+4 y=t \\ x^{\prime }+y^{\prime }-x-y=1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+5 y=4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x+5 y=t^{2} \\ x^{\prime }+2 y^{\prime }-2 x+4 y=2 t +1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+y=t^{2}+4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 t^{2}-2 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+2 y^{\prime }-x+y=t -1 \\ x^{\prime }+y^{\prime }-x=t +2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+4 y^{\prime }+x-y=3 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+2 x+2 y={\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=-2 t \\ x^{\prime }+y^{\prime }+x-y=t^{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=1 \\ x^{\prime }+y^{\prime }+2 x-y=t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+3 y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+2 y+5 t \\ y^{\prime }=3 x+4 y+17 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+7 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=7 x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=2 x+3 y-4 z \\ z^{\prime }=4 x+y-4 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y-z \\ y^{\prime }=x+3 y+z \\ z^{\prime }=-3 x-6 y+6 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+7 y \\ y^{\prime }=3 x+5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+b y \\ y^{\prime }=c x+d y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-4 y-x \left (x^{2}+y^{2}\right ) \\ y^{\prime }=4 x+4 y-y \left (x^{2}+y^{2}\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\ y^{\prime }=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{2} \\ y^{\prime }=2 y-y^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-y \\ y^{\prime }=2 x+y+t^{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y+\cos \left (2 t \right ) \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=6 x+3 y+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y+{\mathrm e}^{3 t} \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+5 y \\ y^{\prime }=-2 x+\cos \left (3 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+{\mathrm e}^{-t} \\ y^{\prime }=4 x-2 y+{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+14 y \\ y^{\prime }=7 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+14 y \\ y^{\prime }=7 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=-5 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=11 x-2 y \\ y^{\prime }=3 x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+20 y \\ y^{\prime }=40 x-19 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+2 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-6 x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-11 x-2 y \\ y^{\prime }=13 x-9 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-5 y \\ y^{\prime }=10 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 x+2 y \\ y^{\prime }=-2 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-y \\ y^{\prime }=x-5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=13 x \\ y^{\prime }=13 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-4 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=y-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x+y={\mathrm e}^{t} \\ y^{\prime }-x-3 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=\frac {y^{2}}{x} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=\frac {x}{2}-\frac {3 y}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-x+2 y=0 \\ y^{\prime }+y-x=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x-2 y=0 \\ 2 x+y^{\prime }-y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-3 x+2 y=0 \\ y^{\prime }-x+3 y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x-z=0 \\ x+y^{\prime }-y=0 \\ z^{\prime }+x+2 y-3 z=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{2}+2 y-3 z \\ y^{\prime }=y-\frac {z}{2} \\ z^{\prime }=-2 x+z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }=y \\ x^{\prime }-y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 y^{\prime }=t \\ x^{\prime }-y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y^{\prime }=x+y-t \\ 2 x^{\prime }+3 y^{\prime }=2 x+6 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }-y^{\prime }=t \\ 3 x^{\prime }+2 y^{\prime }=y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 5 x^{\prime }-3 y^{\prime }=x+y \\ 3 x^{\prime }-y^{\prime }=t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-4 y^{\prime }=0 \\ 2 x^{\prime }-3 y^{\prime }=t +y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+2 y^{\prime }=\sin \left (t \right ) \\ x^{\prime }-2 y^{\prime }=x+y+t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+9 y+12 \,{\mathrm e}^{-t} \\ y^{\prime }=-5 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+6 y+6 \,{\mathrm e}^{-t} \\ y^{\prime }=-12 x+5 y+37 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+10 y+18 \,{\mathrm e}^{t} \\ y^{\prime }=-10 x+9 y+37 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-14 x+39 y+78 \sinh \left (t \right ) \\ y^{\prime }=-6 x+16 y+6 \cosh \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y-2 z-2 \sinh \left (t \right ) \\ y^{\prime }=4 x+2 y-2 z+10 \cosh \left (t \right ) \\ z^{\prime }=-x+3 y+z+5 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+6 y-2 z+50 \,{\mathrm e}^{t} \\ y^{\prime }=6 x+2 y-2 z+21 \,{\mathrm e}^{-t} \\ z^{\prime }=-x+6 y+z+9 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y+4 z \\ y^{\prime }=-2 x+y+2 z \\ z^{\prime }=-4 x-2 y+6 z+{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y+3 z \\ y^{\prime }=x-y+2 z+2 \,{\mathrm e}^{-t} \\ z^{\prime }=-2 x+2 y-2 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+y-1-6 \,{\mathrm e}^{t} \\ y^{\prime }=-4 x+3 y+4 \,{\mathrm e}^{t}-3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y+24 \sin \left (t \right ) \\ y^{\prime }=9 x-3 y+12 \cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x-4 y+10 \,{\mathrm e}^{t} \\ y^{\prime }=3 x+14 y+6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-7 x+4 y+6 \,{\mathrm e}^{3 t} \\ y^{\prime }=-5 x+2 y+6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-3 y+z \\ y^{\prime }=2 y+2 z+29 \,{\mathrm e}^{-t} \\ z^{\prime }=5 x+y+z+39 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-z+5 \sin \left (t \right ) \\ y^{\prime }=y+z-10 \cos \left (t \right ) \\ z^{\prime }=x+z+2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+3 y+z+5 \sin \left (2 t \right ) \\ y^{\prime }=x-5 y-3 z+5 \cos \left (2 t \right ) \\ z^{\prime }=-3 x+7 y+3 z+23 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y-3 z+2 \,{\mathrm e}^{t} \\ y^{\prime }=4 x-y+2 z+4 \,{\mathrm e}^{t} \\ z^{\prime }=4 x-2 y+3 z+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+5 y+10 \sinh \left (t \right ) \\ y^{\prime }=19 x-13 y+24 \sinh \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 x-3 y-6 t \\ y^{\prime }=-x+11 y+10 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+1 \\ y^{\prime }=1+x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }-y^{\prime }+3 x=\sin \left (t \right ) \\ x^{\prime }+y=\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-3 y \\ y^{\prime }=5 x+6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-10 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=12 x+18 y \\ y^{\prime }=-8 x-12 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+2 y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=2 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=2 x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}-2 y_{2} \\ y_{2}^{\prime }=y_{1}+3 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2}+x -1 \\ y_{2}^{\prime }=3 y_{1}+2 y_{2}-5 x -2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {2 y_{1}}{x}-\frac {y_{2}}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}} \\ y_{2}^{\prime }=2 y_{1}+1-6 x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}-2 y_{2} \\ y_{2}^{\prime }=y_{2}-y_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\sin \left (x \right ) y_{1}+\sqrt {x}\, y_{2}+\ln \left (x \right ) \\ y_{2}^{\prime }=\tan \left (x \right ) y_{1}-{\mathrm e}^{x} y_{2}+1 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\ y_{2}^{\prime }=\frac {y_{1}}{\left (-2+x \right )^{2}} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }={\mathrm e}^{-x} y_{1}-\sqrt {x +1}\, y_{2}+x^{2} \\ y_{2}^{\prime }=\frac {y_{1}}{\left (-2+x \right )^{2}} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2}+5 \,{\mathrm e}^{x} \\ y_{2}^{\prime }=y_{1}+4 y_{2}-2 \,{\mathrm e}^{-x} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}-2 y_{1}+\sin \left (2 x \right ) \\ y_{2}^{\prime }=-3 y_{1}+y_{2}-2 \cos \left (3 x \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2} \\ y_{2}^{\prime }=3 y_{1} \\ y_{3}^{\prime }=2 y_{3}-y_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 x y_{1}-x^{2} y_{2}+4 x \\ y_{2}^{\prime }={\mathrm e}^{x} y_{1}+3 \,{\mathrm e}^{-x} y_{2}-\cos \left (3 x \right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-3 y_{2}+4 x -2 \\ y_{2}^{\prime }=y_{1}-2 y_{2}+3 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x} \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=\frac {5 y_{1}}{x}+\frac {4 y_{2}}{x}-2 x \\ y_{2}^{\prime }=-\frac {6 y_{1}}{x}-\frac {5 y_{2}}{x}+5 x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2}-2 y_{3} \\ y_{2}^{\prime }=3 y_{2}-2 y_{3} \\ y_{3}^{\prime }=3 y_{1}+y_{2}-3 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-5 y_{2}-5 y_{3} \\ y_{2}^{\prime }=-y_{1}+4 y_{2}+2 y_{3} \\ y_{3}^{\prime }=3 y_{1}-5 y_{2}-3 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}+6 y_{2}+6 y_{3} \\ y_{2}^{\prime }=y_{1}+3 y_{2}+2 y_{3} \\ y_{3}^{\prime }=-y_{1}-4 y_{2}-3 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2}-3 y_{3} \\ y_{2}^{\prime }=-3 y_{1}+4 y_{2}-2 y_{3} \\ y_{3}^{\prime }=2 y_{1}+y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }=-y_{1}-2 y_{2}-y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}-2 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+y_{2}+2 y_{3} \\ y_{2}^{\prime }=y_{1}+y_{2}+2 y_{3} \\ y_{3}^{\prime }=2 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2} \\ y_{2}^{\prime }=-y_{1}+2 y_{2} \\ y_{3}^{\prime }=3 y_{3}-4 y_{4} \\ y_{4}^{\prime }=4 y_{3}+3 y_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2} \\ y_{2}^{\prime }=-3 y_{1}+2 y_{3} \\ y_{3}^{\prime }=y_{4} \\ y_{4}^{\prime }=2 y_{1}-5 y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+2 y_{2} \\ y_{2}^{\prime }=3 y_{2}-2 y_{1} \\ y_{3}^{\prime }=y_{3} \\ y_{4}^{\prime }=2 y_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}+y_{4} \\ y_{2}^{\prime }=y_{1}-y_{3} \\ y_{3}^{\prime }=y_{4} \\ y_{4}^{\prime }=y_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=5 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x-y+2 \\ y^{\prime }=3 x-y-3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y-6 \\ y^{\prime }=4 x-y+2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 y \\ y^{\prime }=3 \pi y-\frac {x}{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} p^{\prime }=3 p-2 q-7 r \\ q^{\prime }=-2 p+6 r \\ r^{\prime }=\frac {73 q}{100}+2 r \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+2 \pi y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\beta y \\ y^{\prime }=\gamma x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=2 x-5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-3 y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=1 \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-2 y \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x-2 y \\ y^{\prime }=-x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{2} \\ y^{\prime }=x-\frac {y}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=9 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=y-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=-4 x+6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-5 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-6 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+4 y \\ y^{\prime }=-3 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=-4 x+6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-5 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-6 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+4 y \\ y^{\prime }=-3 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {9 x}{10}-2 y \\ y^{\prime }=x+\frac {11 y}{10} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+10 y \\ y^{\prime }=-x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y \\ y^{\prime }=3 x+6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{10} \\ y^{\prime }=\frac {z}{5} \\ z^{\prime }=\frac {2 x}{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \\ z^{\prime }=2 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=3 x-2 y \\ z^{\prime }=-z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 z \\ y^{\prime }=-y \\ z^{\prime }=-3 x+z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 y-z \\ z^{\prime }=-y+2 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y \\ z^{\prime }=-z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y \\ z^{\prime }=z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-4 y \\ z^{\prime }=-z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-4 y \\ z^{\prime }=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y+z \\ z^{\prime }=-2 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-2 y+3 z \\ z^{\prime }=-x+3 y-z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+3 y \\ y^{\prime }=z-y \\ z^{\prime }=5 x-5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-10 x+10 y \\ y^{\prime }=28 x-y \\ z^{\prime }=-\frac {8 z}{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z-y \\ y^{\prime }=z-x \\ z^{\prime }=z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\pi ^{2} x+\frac {187 y}{5} \\ y^{\prime }=\sqrt {555}\, x+\frac {400617 y}{5000} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=y-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=-2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-4 x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x-3 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=1-2 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=6 x-7 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+2 x=15 y \\ t y^{\prime }=x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=2 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=8 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+2 y-17 \\ y^{\prime }=4 x+y-13 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x+2 y+7 \,{\mathrm e}^{2 t} \\ y^{\prime }=4 x+y-7 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+3 y-6 \,{\mathrm e}^{3 t} \\ y^{\prime }=x+6 y+2 \,{\mathrm e}^{3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=4 x+24 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x+19 \cos \left (4 t \right )-13 \sin \left (4 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+3 y+5 \operatorname {Heaviside}\left (t -2\right ) \\ y^{\prime }=x+6 y+17 \operatorname {Heaviside}\left (t -2\right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=3 x-7 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y+4 \\ y^{\prime }=3 x-7 y+5 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=6 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x y-6 y \\ y^{\prime }=x-y-5 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-4 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+4 y \\ y^{\prime }=2 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 \\ y^{\prime }=\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2} \\ y^{\prime }={\mathrm e}^{t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1} \\ x_{2}^{\prime }=1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+1 \\ x_{2}^{\prime }=x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+6 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 x-y \\ y^{\prime }=x+6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=-x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\sin \left (2 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 t x_{1}^{2} \\ x_{2}^{\prime }=\frac {x_{2}+t}{t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }={\mathrm e}^{t -x_{1}} \\ x_{2}^{\prime }=2 \,{\mathrm e}^{x_{1}} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=\frac {y^{2}}{x} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}^{2}}{x_{2}} \\ x_{2}^{\prime }=x_{2}-x_{1} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {{\mathrm e}^{-x}}{t} \\ y^{\prime }=\frac {x \,{\mathrm e}^{-y}}{t} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {t +y}{x+y} \\ y^{\prime }=\frac {x-t}{x+y} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {t -y}{y-x} \\ y^{\prime }=\frac {x-t}{y-x} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {t +y}{x+y} \\ y^{\prime }=\frac {t +x}{x+y} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-9 y \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=t +y \\ y^{\prime }=x-t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+3 x+4 y=0 \\ y^{\prime }+2 x+5 y=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+5 y \\ y^{\prime }=-x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }-y^{\prime }+3 x=\sin \left (t \right ) \\ x^{\prime }+y=\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z-y \\ y^{\prime }=z \\ z^{\prime }=z-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z \\ y^{\prime }=x+z \\ z^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=y \\ y^{\prime \prime }=x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }+y^{\prime }+x=0 \\ x^{\prime }+y^{\prime \prime }=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=3 x+y \\ y^{\prime }=-2 x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=x^{2}+y \\ y^{\prime }=-2 x x^{\prime }+x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2} \\ y^{\prime }=2 x y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {1}{y} \\ y^{\prime }=\frac {1}{x} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {x}{y} \\ y^{\prime }=\frac {y}{x} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {y}{x-y} \\ y^{\prime }=\frac {x}{x-y} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\sin \left (x\right ) \cos \left (y\right ) \\ y^{\prime }=\cos \left (x\right ) \sin \left (y\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} {\mathrm e}^{t} x^{\prime }=\frac {1}{y} \\ {\mathrm e}^{t} y^{\prime }=\frac {1}{x} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\ y^{\prime }=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=8 y-x \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=y-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y \\ y^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z-x \\ y^{\prime }=x-y+z \\ z^{\prime }=x+y-z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y+z \\ y^{\prime }=x+2 y-z \\ z^{\prime }=x-y+2 z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y+z \\ y^{\prime }=x+z \\ z^{\prime }=y-2 z-3 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x-y=-{\mathrm e}^{2 t} \\ y^{\prime }+3 x-2 y=6 \,{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-\cos \left (t \right ) \\ y^{\prime }=-y-2 x+\cos \left (t \right )+\sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+\tan \left (t \right )^{2}-1 \\ y^{\prime }=\tan \left (t \right )-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\ y^{\prime }=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\frac {1}{\cos \left (t \right )} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3-2 y \\ y^{\prime }=2 x-2 t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y+\sin \left (t \right ) \\ y^{\prime }=x+\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+{\mathrm e}^{t} \\ y^{\prime }=x+y-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y+4 t -1 \\ y^{\prime }=x-2 y+t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x+{\mathrm e}^{t} \\ y^{\prime }=x-y+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y=t^{2} \\ -x+y^{\prime }=t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }+y={\mathrm e}^{-t} \\ 2 x^{\prime }+y^{\prime }+2 y=\sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-2 z+2-t \\ y^{\prime }=-x+1 \\ z^{\prime }=x+y-z+1-t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x+2 y=2 \,{\mathrm e}^{-t} \\ y^{\prime }+y+z=1 \\ z^{\prime }+z=1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x+y \\ y^{\prime }=4 x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y+1 \\ y^{\prime }=-x+5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+y+{\mathrm e}^{t} \\ y^{\prime }=x+3 y-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y+\cos \left (t \right ) \\ y^{\prime }=-x-2 y+\sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x+4 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+\sin \left (t \right ) \\ y^{\prime }=-x+y-\cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x t +y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+4 \\ y^{\prime }=-2 x+y-3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+t y \\ y^{\prime }=x t -y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+4 \\ y^{\prime }=-2 x+\sin \left (t \right ) y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+2 \sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y+2 t \\ y^{\prime }=x-3 y-3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y+1 \\ y^{\prime }=x+y-3 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y-4 \\ y^{\prime }=x-y-6 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{4}-\frac {3 y}{4}+8 \\ y^{\prime }=\frac {x}{2}+y-\frac {23}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y-11 \\ y^{\prime }=-5 x+4 y-35 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-3 \\ y^{\prime }=-x+y+1 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+4 y-35 \\ y^{\prime }=-2 x+y-11 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=4 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=\frac {3 x}{4}+\frac {5 y}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {3 x}{4}-\frac {7 y}{4} \\ y^{\prime }=\frac {x}{4}+\frac {5 y}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{4}-\frac {3 y}{4} \\ y^{\prime }=\frac {x}{2}+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-5 x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+6 y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-5 x+4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-\frac {5 y}{2} \\ y^{\prime }=\frac {9 x}{5}-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=5 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=-5 x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+2 y \\ y^{\prime }=-x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {3 x}{4}-2 y \\ y^{\prime }=x-\frac {5 y}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {4 x}{5}+2 y \\ y^{\prime }=-x+\frac {6 y}{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+y \\ y^{\prime }=-x+a y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 y \\ y^{\prime }=x+a y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=a x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=a x+\frac {5 y}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+a y \\ y^{\prime }=-x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+a y \\ y^{\prime }=-6 x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+10 y \\ y^{\prime }=-x-4 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+a y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} i^{\prime }=\frac {i}{2}-\frac {v}{8} \\ v^{\prime }=2 i-\frac {v}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=-\frac {3 x}{4}-\frac {y}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {3 x}{2}+y \\ y^{\prime }=-\frac {x}{4}-\frac {y}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+\frac {5 y}{2} \\ y^{\prime }=-\frac {5 x}{2}+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-\frac {y}{2} \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+\frac {y}{2} \\ y^{\prime }=-\frac {x}{2}+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {5 x}{2}+\frac {3 y}{2} \\ y^{\prime }=-\frac {3 x}{2}+\frac {y}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+\frac {3 y}{2} \\ y^{\prime }=-\frac {3 x}{2}-y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=-\frac {3 x}{4}-\frac {y}{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+\frac {5 y}{2} \\ y^{\prime }=-\frac {5 x}{2}+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+\frac {y}{2} \\ y^{\prime }=-\frac {x}{2}+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=8 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=8 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-8 x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y+x^{2} \\ y^{\prime }=y-2 x y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 y \,x^{2}-3 x^{2}-4 y \\ y^{\prime }=-2 x \,y^{2}+6 x y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-x^{2} \\ y^{\prime }=2 x y-3 y+2 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x y \\ y^{\prime }=y+2 x y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2-y \\ y^{\prime }=y-x^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-x^{2}-x y \\ y^{\prime }=\frac {y}{2}-\frac {y^{2}}{4}-\frac {3 x y}{4} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\left (x-y\right ) \left (1-x-y\right ) \\ y^{\prime }=x \left (2+y\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \left (2-x-y\right ) \\ y^{\prime }=-x-y-2 x y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\left (x+2\right ) \left (y-x\right ) \\ y^{\prime }=y-x^{2}-y^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 x y \\ y^{\prime }=y-x^{2}-y^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x-\frac {x^{3}}{5}-\frac {y}{5} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (1-x-y\right ) \\ y^{\prime }=y \left (\frac {3}{4}-y-\frac {x}{2}\right ) \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-5 y_{1}+y_{2} \\ y_{2}^{\prime }=-9 y_{1}+5 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-2 y_{2} \\ y_{2}^{\prime }=6 y_{1}-2 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-4 y_{2} \\ y_{2}^{\prime }=5 y_{1}-4 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=6 y_{2} \\ y_{2}^{\prime }=-6 y_{1} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-4 y_{1}-y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-64 y_{2} \\ y_{2}^{\prime }=y_{1}-14 y_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-4 y_{1}-y_{2}+2 \,{\mathrm e}^{t} \\ y_{2}^{\prime }=y_{1}-2 y_{2}+\sin \left (2 t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-y_{2}+{\mathrm e}^{-t} \\ y_{2}^{\prime }=y_{1}+3 y_{2}+2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-5 y_{2}+3 \\ y_{2}^{\prime }=y_{1}+3 y_{2}+5 \cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2}+\sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}-y_{3} \\ y_{2}^{\prime }=y_{1}+y_{3}-{\mathrm e}^{-t} \\ y_{3}^{\prime }=y_{1}+y_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+x_{2} \\ x_{2}^{\prime }=x_{1}-5 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{2}-4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+4 x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{2}+2 x_{3} \\ x_{3}^{\prime }=2 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-4 x_{1}+2 x_{2}-2 x_{3} \\ x_{3}^{\prime }=2 x_{1}-2 x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }=-2 x_{1}+3 x_{2}-2 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+4 x_{2}-3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+6 x_{3} \\ x_{2}^{\prime }=x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }=6 x_{1}+x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-8 x_{1}-5 x_{2}-3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{2}^{\prime }=2 x_{2}+2 x_{3} \\ x_{3}^{\prime }=-x_{1}+x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{3} \\ x_{2}^{\prime }=2 x_{1} \\ x_{3}^{\prime }=-x_{1}+2 x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{3} \\ x_{2}^{\prime }=-2 x_{2} \\ x_{3}^{\prime }=3 x_{1}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}-x_{2}-\frac {3 x_{3}}{2} \\ x_{2}^{\prime }=\frac {3 x_{1}}{2}-2 x_{2}-\frac {3 x_{3}}{2} \\ x_{3}^{\prime }=-2 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+5 x_{2}+3 x_{3}-5 x_{4} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2}+2 x_{3}-4 x_{4} \\ x_{3}^{\prime }=-x_{2}-2 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{1}+4 x_{2}+2 x_{3}-5 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}+x_{2}-4 x_{3}-x_{4} \\ x_{2}^{\prime }=-3 x_{2} \\ x_{3}^{\prime }=x_{1}-x_{2}+x_{4} \\ x_{4}^{\prime }=2 x_{1}-x_{2}+2 x_{3}-2 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+2 x_{2}-x_{4} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+2 x_{4} \\ x_{3}^{\prime }=3 x_{3} \\ x_{4}^{\prime }=-x_{1}+2 x_{2}+2 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+8 x_{2}+5 x_{3}+3 x_{4} \\ x_{2}^{\prime }=2 x_{1}+16 x_{2}+10 x_{3}+6 x_{4} \\ x_{3}^{\prime }=5 x_{1}-14 x_{2}-11 x_{3}-3 x_{4} \\ x_{4}^{\prime }=-x_{1}-8 x_{2}-5 x_{3}-3 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+2 x_{2}-2 x_{4} \\ x_{2}^{\prime }=-x_{1}+3 x_{2}-x_{3}+x_{4} \\ x_{3}^{\prime }=-2 x_{1}-2 x_{2}-4 x_{3}+2 x_{4} \\ x_{4}^{\prime }=-7 x_{1}+x_{2}-7 x_{3}+3 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-5 x_{1}-2 x_{2}-x_{3}+2 x_{4}+3 x_{5} \\ x_{2}^{\prime }=-3 x_{2} \\ x_{3}^{\prime }=x_{1}-x_{3}-x_{5} \\ x_{4}^{\prime }=2 x_{1}+x_{2}-4 x_{4}-2 x_{5} \\ x_{5}^{\prime }=-3 x_{1}-2 x_{2}-x_{3}+2 x_{4}+x_{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{2}-2 x_{3}+3 x_{4}+2 x_{5} \\ x_{2}^{\prime }=8 x_{1}+6 x_{2}+4 x_{3}-8 x_{4}-16 x_{5} \\ x_{3}^{\prime }=-8 x_{1}-8 x_{2}-6 x_{3}+8 x_{4}-16 x_{5} \\ x_{4}^{\prime }=8 x_{1}+7 x_{2}+4 x_{3}-9 x_{4}-16 x_{5} \\ x_{5}^{\prime }=-3 x_{1}-5 x_{2}-3 x_{3}+5 x_{4}+7 x_{5} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+2 x_{2}+x_{3} \\ x_{2}^{\prime }=-2 x_{1}+2 x_{2}+2 x_{3} \\ x_{3}^{\prime }=2 x_{1}-3 x_{2}-3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-4 x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+3 x_{3} \\ x_{3}^{\prime }=3 x_{1}-4 x_{2}-2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-2 x_{2}-2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+2 x_{2}-x_{3} \\ x_{2}^{\prime }=-6 x_{1}-3 x_{3} \\ x_{3}^{\prime }=\frac {8 x_{2}}{3}-2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+6 x_{2}-6 x_{3} \\ x_{2}^{\prime }=-9 x_{1}+5 x_{2}-9 x_{3} \\ x_{3}^{\prime }=-x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {4 x_{1}}{3}+\frac {4 x_{2}}{3}-\frac {11 x_{3}}{3} \\ x_{2}^{\prime }=-\frac {16 x_{1}}{3}-\frac {x_{2}}{3}+\frac {14 x_{3}}{3} \\ x_{3}^{\prime }=3 x_{1}-2 x_{2}-2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-8 x_{1}-5 x_{2}-3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {3 x_{1}}{4}+\frac {29 x_{2}}{4}-\frac {11 x_{3}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{4}+\frac {3 x_{2}}{4}-\frac {5 x_{3}}{2} \\ x_{3}^{\prime }=\frac {5 x_{1}}{4}+\frac {11 x_{2}}{4}-\frac {5 x_{3}}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-x_{2}+4 x_{3}+2 x_{4} \\ x_{2}^{\prime }=-19 x_{1}-6 x_{2}+6 x_{3}+16 x_{4} \\ x_{3}^{\prime }=-9 x_{1}-x_{2}+x_{3}+6 x_{4} \\ x_{4}^{\prime }=-5 x_{1}-3 x_{2}+6 x_{3}+5 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+6 x_{2}+2 x_{3}-2 x_{4} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2}-6 x_{3}+2 x_{4} \\ x_{3}^{\prime }=-4 x_{1}+8 x_{2}+3 x_{3}-4 x_{4} \\ x_{4}^{\prime }=2 x_{1}-2 x_{2}-6 x_{3}+x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-4 x_{2}+5 x_{3}+9 x_{4} \\ x_{2}^{\prime }=-2 x_{1}-5 x_{2}+4 x_{3}+12 x_{4} \\ x_{3}^{\prime }=-2 x_{1}-x_{3}+2 x_{4} \\ x_{4}^{\prime }=-2 x_{2}+2 x_{3}+3 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-5 x_{2}+8 x_{3}+14 x_{4} \\ x_{2}^{\prime }=-6 x_{1}-8 x_{2}+11 x_{3}+27 x_{4} \\ x_{3}^{\prime }=-6 x_{1}-4 x_{2}+7 x_{3}+17 x_{4} \\ x_{4}^{\prime }=-2 x_{2}+2 x_{3}+4 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{2}-2 x_{4} \\ x_{2}^{\prime }=-\frac {x_{1}}{2}+x_{2}-3 x_{3}-\frac {5 x_{4}}{2} \\ x_{3}^{\prime }=3 x_{2}-5 x_{3}-3 x_{4} \\ x_{4}^{\prime }=x_{1}+3 x_{2}-3 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=\frac {x_{1}}{2}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}-\frac {x_{2}}{4} \\ x_{2}^{\prime }=x_{1}-\frac {x_{2}}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {x_{1}}{2}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}}{2}+\frac {x_{2}}{2} \\ x_{2}^{\prime }=2 x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+4 x_{2} \\ x_{2}^{\prime }=-x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {5 x_{1}}{2}+2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-8 x_{1}-5 x_{2}-3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}+4 x_{3} \\ x_{2}^{\prime }=3 x_{1}+2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-k_{1} x_{1} \\ x_{2}^{\prime }=k_{1} x_{1}-k_{2} x_{2} \\ x_{3}^{\prime }=k_{2} x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}+t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sin \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=1-x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{2}+t \\ x_{3}^{\prime }=-2 x_{1}-x_{2}+3 x_{3}+{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {x_{3}}{2}+1 \\ x_{2}^{\prime }=-x_{1}-2 x_{2}+x_{3}+t \\ x_{3}^{\prime }=\frac {x_{1}}{2}+\frac {x_{2}}{2}-\frac {3 x_{3}}{2}+11 \,{\mathrm e}^{-3 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+x_{2}+3 x_{3}+3 t \\ x_{2}^{\prime }=-2 x_{2} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}+x_{3}+3 \cos \left (t \right ) \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}+x_{2}+\frac {x_{3}}{2} \\ x_{2}^{\prime }=x_{1}-x_{2}+x_{3}-\sin \left (t \right ) \\ x_{3}^{\prime }=\frac {x_{1}}{2}+x_{2}-\frac {x_{3}}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+1 \\ x_{2}^{\prime }=x_{1}-2 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-3 x_{2}-2 x_{3} \\ x_{2}^{\prime }=8 x_{1}-5 x_{2}-4 x_{3} \\ x_{3}^{\prime }=-4 x_{1}+3 x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+9 x_{2}-6 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+11 x_{2}-7 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+3 x_{2}-x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}+6 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2}-x_{3} \\ x_{3}^{\prime }=-2 x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-8 x_{1}-16 x_{2}-16 x_{3}-17 x_{4} \\ x_{2}^{\prime }=-2 x_{1}-10 x_{2}-8 x_{3}-7 x_{4} \\ x_{3}^{\prime }=-2 x_{1}-2 x_{3}-3 x_{4} \\ x_{4}^{\prime }=6 x_{1}+14 x_{2}+14 x_{3}+14 x_{4} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-2 x_{3}+3 x_{4} \\ x_{2}^{\prime }=2 x_{1}-\frac {3 x_{2}}{2}-x_{3}+\frac {7 x_{4}}{2} \\ x_{3}^{\prime }=-x_{1}+\frac {x_{2}}{2}-\frac {3 x_{4}}{2} \\ x_{4}^{\prime }=-2 x_{1}+\frac {3 x_{2}}{2}+3 x_{3}-\frac {7 x_{4}}{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=6 x_{1}+4 x_{2}+6 x_{3} \\ x_{3}^{\prime }=-5 x_{1}-2 x_{2}-4 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=-14 x_{1}-5 x_{2}+x_{3} \\ x_{3}^{\prime }=15 x_{1}+5 x_{2}-2 x_{3} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 y+x y \\ y^{\prime }=x+4 x y \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=1+5 y \\ y^{\prime }=1-6 x^{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=y+z \\ z^{\prime }=y+z+x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=\frac {y^{2}}{z} \\ z^{\prime }=\frac {y}{2} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=1-\frac {1}{z} \\ z^{\prime }=\frac {1}{y-x} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=-z \\ z^{\prime }=y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=\frac {z^{2}}{y} \\ z^{\prime }=\frac {y^{2}}{z} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }=\frac {y^{2}}{z} \\ z^{\prime }=\frac {z^{2}}{y} \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+z-x \\ y^{\prime }=x-y+z \\ z^{\prime }=x+y-z \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+x+y=t^{2} \\ y^{\prime }+y+z=2 t \\ z^{\prime }+z=t \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x+y=7 \,{\mathrm e}^{t}-27 \\ -2 x+y^{\prime }+3 y=-3 \,{\mathrm e}^{t}+12 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime \prime }+z^{\prime }-2 z={\mathrm e}^{2 x} \\ z^{\prime }+2 y^{\prime }-3 y=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x+{\mathrm e}^{t}+{\mathrm e}^{-t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+\frac {2 z}{x^{2}}=1 \\ z^{\prime }+y=x \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }-x-3 y=t \\ t y^{\prime }-x+y=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+6 x-y-3 z=0 \\ t y^{\prime }+23 x-6 y-9 z=0 \\ t z^{\prime }+x+y-2 z=0 \end {array}\right ]
\] |
✗ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+5 x+y={\mathrm e}^{t} \\ y^{\prime }-x+3 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+t -1 \\ y^{\prime }=3 x+2 y-5 t -2 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=y-x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+6 y \\ y^{\prime }=2 x+6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-5 t +2 \\ y^{\prime }=4 x-2 y-8 t -8 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=4 x-5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+2 y \\ y^{\prime }=-17 x-5 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+7 y-3 z=0 \\ 7 y^{\prime }+63 y-36 z=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+2 y^{\prime }+3 y=0 \\ y^{\prime }+3 y-2 z=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+3 y+z=0 \\ z^{\prime }+3 y+5 z=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+3 y+2 z=0 \\ z^{\prime }+2 y-4 z=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }-3 y-2 z=0 \\ z^{\prime }+y-2 z=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }+z^{\prime }+6 y=0 \\ z^{\prime }+5 y+z=0 \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+y^{\prime }+5 y-3 z=x +{\mathrm e}^{x} \\ y^{\prime }+2 y-z={\mathrm e}^{x} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+y+3 z={\mathrm e}^{x} \\ y^{\prime }+3 y+4 z={\mathrm e}^{2 x} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }-3 y+2 z={\mathrm e}^{x} \\ y^{\prime }+2 y-z={\mathrm e}^{3 x} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+5 y-2 z=x \\ y^{\prime }+4 y+z=x \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} z^{\prime }+7 y-9 z={\mathrm e}^{x} \\ y^{\prime }-y-3 z={\mathrm e}^{2 x} \end {array}\right ]
\] |
✓ |
|
|
\[
{}\left [\begin {array}{c} y^{\prime }-2 y-2 z={\mathrm e}^{3 x} \\ z^{\prime }+5 y-2 z={\mathrm e}^{4 x} \end {array}\right ]
\] |
✓ |
|