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ODE |
Solved? |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=-2 x_{1}+2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2}+t \\ x_{2}^{\prime }=2 x_{1}-2 x_{2}+3 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=4 x_{1}+x_{2}-{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}-x_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\tan \left (t \right ) \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+f_{1} \left (t \right ) \\ x_{2}^{\prime }=-x_{1}+f_{2} \left (t \right ) \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2}+\delta \left (t -\pi \right ) \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2}+1-\operatorname {Heaviside}\left (t -\pi \right ) \\ x_{2}^{\prime }=2 x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+4 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{2} \\ x_{3}^{\prime }=3 x_{3}+{\mathrm e}^{2 t} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}+2 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}+3 x_{3} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right ) \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=3 x_{3} \\ x_{4}^{\prime }=2 x_{3}+3 x_{4} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }-x-2 y=16 t \,{\mathrm e}^{t} \\ 2 x-y^{\prime }-2 y=0 \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }-2 x+y=5 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x+y^{\prime }-2 y=10 \,{\mathrm e}^{t} \sin \left (t \right ) \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }-4 x+3 y=\sin \left (t \right ) \\ 2 x+y^{\prime }-y=2 \cos \left (t \right ) \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }-2 x-y=2 \,{\mathrm e}^{t} \\ x-y^{\prime }+2 y=3 \,{\mathrm e}^{4 t} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime \prime }+x^{\prime }+y^{\prime }-2 y=40 \,{\mathrm e}^{3 t} \\ x^{\prime }+x-y^{\prime }=36 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✗ |
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\[
{}\left [\begin {array}{c} x^{\prime }-2 x-y=2 \,{\mathrm e}^{t} \\ y^{\prime }-2 y-4 z=4 \,{\mathrm e}^{2 t} \\ x-z^{\prime }-z=0 \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime \prime }+2 x-2 y^{\prime }=0 \\ 3 x^{\prime }+y^{\prime \prime }-8 y=240 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✗ |
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\[
{}\left [\begin {array}{c} x^{\prime }-x-2 y=0 \\ x-y^{\prime }=15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x^{\prime }-x+y=2 \sin \left (t \right ) \left (1-\operatorname {Heaviside}\left (t -\pi \right )\right ) \\ 2 x-y^{\prime }-y=0 \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} 2 x^{\prime }+x-5 y^{\prime }-4 y=28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right ) \\ 3 x^{\prime }-2 x-4 y^{\prime }+y=0 \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-5 y_{1}+y_{2} \\ y_{2}^{\prime }=-9 y_{1}+5 y_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-2 y_{2} \\ y_{2}^{\prime }=6 y_{1}-2 y_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-4 y_{2} \\ y_{2}^{\prime }=5 y_{1}-4 y_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} y_{1}^{\prime }=6 y_{2} \\ y_{2}^{\prime }=-6 y_{1} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-4 y_{1}-y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}-64 y_{2} \\ y_{2}^{\prime }=y_{1}-14 y_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-4 y_{1}-y_{2}+2 \,{\mathrm e}^{t} \\ y_{2}^{\prime }=y_{1}-2 y_{2}+\sin \left (2 t \right ) \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-y_{2}+{\mathrm e}^{-t} \\ y_{2}^{\prime }=y_{1}+3 y_{2}+2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-5 y_{2}+3 \\ y_{2}^{\prime }=y_{1}+3 y_{2}+5 \cos \left (t \right ) \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2}+\sin \left (t \right ) \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} y_{1}^{\prime }=y_{2}-y_{3} \\ y_{2}^{\prime }=y_{1}+y_{3}-{\mathrm e}^{-t} \\ y_{3}^{\prime }=y_{1}+y_{2}+{\mathrm e}^{t} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ]
\] |
✓ |
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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \end {array}\right ]
\] |
✓ |
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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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\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
✓ |
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