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# |
ODE |
Mathematica |
Maple |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+5 x_{4} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )+x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-5 x_{2} \left (t \right )+{\mathrm e}^{-t}]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )-2 x_{2} \left (t \right )+9 t, x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = 10 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+\frac {{\mathrm e}^{6 t}}{t}\right ]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right )+3 x_{3} \left (t \right )+{\mathrm e}^{6 t}, x_{2}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )-3 x_{2} \left (t \right )-9 x_{3} \left (t \right )+1, x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right )+t, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+1]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -6 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-7 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 10 x_{1} \left (t \right )-8 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{2} \left (x \right )-2 y_{1} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{2} \left (x \right )-y_{1} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+3 y_{2} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 4 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 4 y_{2} \left (x \right )-y_{1} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{2} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right )-y_{1} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )-4 y_{2} \left (x \right )]
\] |
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\[
{}[2 y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right ), 2 y_{2}^{\prime }\left (x \right ) = 5 y_{2} \left (x \right )-3 y_{1} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = -2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+2 y_{2} \left (x \right )]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 1, y_{2}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )]
\] |
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\[
{}[2 y_{1}^{\prime }\left (x \right )+y_{2}^{\prime }\left (x \right )-4 y_{1} \left (x \right )-y_{2} \left (x \right ) = {\mathrm e}^{x}, y_{1}^{\prime }\left (x \right )+3 y_{1} \left (x \right )+y_{2} \left (x \right ) = 0]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = -y_{2} \left (x \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = 0, x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 0]
\] |
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\[
{}[2 x^{\prime }\left (t \right )+x \left (t \right )-5 y^{\prime }\left (t \right )-4 y \left (t \right ) = 0, -y^{\prime }\left (t \right )-2 x \left (t \right )+y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right ) = 0, 3 x \left (t \right )-y^{\prime }\left (t \right )+y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime \prime }\left (t \right )+x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 0, x^{\prime }\left (t \right )+x \left (t \right )-y^{\prime }\left (t \right ) = 0]
\] |
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\[
{}[x^{\prime \prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right ) = 0, x \left (t \right )+y^{\prime \prime }\left (t \right )+y \left (t \right ) = 0]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right )-y_{2} \left (x \right ) = 0, 4 y_{1} \left (x \right )+y_{2}^{\prime }\left (x \right )-4 y_{2} \left (x \right )-2 y_{3} \left (x \right ) = 0, -2 y_{1} \left (x \right )+y_{2} \left (x \right )+y_{3}^{\prime }\left (x \right )+y_{3} \left (x \right ) = 0]
\] |
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\[
{}[y_{1}^{\prime }\left (x \right )-2 y_{1} \left (x \right )+3 y_{2} \left (x \right )-3 y_{3} \left (x \right ) = 0, -4 y_{1} \left (x \right )+y_{2}^{\prime }\left (x \right )+5 y_{2} \left (x \right )-3 y_{3} \left (x \right ) = 0, -4 y_{1} \left (x \right )+4 y_{2} \left (x \right )+y_{3}^{\prime }\left (x \right )-2 y_{3} \left (x \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right ) = 8, 2 x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 2 \,{\mathrm e}^{-t}-8]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )+t \,{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )+{\mathrm e}^{-t}]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = {\mathrm e}^{t}, -4 x \left (t \right )+y^{\prime }\left (t \right )-3 y \left (t \right ) = 1]
\] |
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\[
{}[x^{\prime }\left (t \right )-4 x \left (t \right )+3 y \left (t \right ) = \sin \left (t \right ), -2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = -2 \cos \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )-y \left (t \right ) = 0, -x \left (t \right )+y^{\prime }\left (t \right ) = {\mathrm e}^{t}+{\mathrm e}^{-t}]
\] |
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\[
{}[x^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right ) = 0, -x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = \sin \left (2 t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )-2 x \left (t \right )+2 y^{\prime }\left (t \right ) = -4 \,{\mathrm e}^{2 t}, 2 x^{\prime }\left (t \right )-3 x \left (t \right )+3 y^{\prime }\left (t \right )-y \left (t \right ) = 0]
\] |
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\[
{}[3 x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )-6 y \left (t \right ) = 5 \,{\mathrm e}^{t}, 4 x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )-8 y \left (t \right ) = 5 \,{\mathrm e}^{t}+2 t -3]
\] |
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\[
{}[x^{\prime }\left (t \right )-5 x \left (t \right )+3 y \left (t \right ) = 2 \,{\mathrm e}^{3 t}, -x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = 5 \,{\mathrm e}^{-t}]
\] |
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\[
{}[x^{\prime }\left (t \right )-2 x \left (t \right )+y \left (t \right ) = 0, x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = -5 \,{\mathrm e}^{t} \sin \left (t \right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right )+4 x \left (t \right )+2 y \left (t \right ) = \frac {2}{{\mathrm e}^{t}-1}, 6 x \left (t \right )-y^{\prime }\left (t \right )+3 y \left (t \right ) = \frac {3}{{\mathrm e}^{t}-1}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = \sec \left (t \right ), -2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = 16 t \,{\mathrm e}^{t}, 2 x \left (t \right )-y^{\prime }\left (t \right )-2 y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )-2 x \left (t \right )+y \left (t \right ) = 5 \,{\mathrm e}^{t} \cos \left (t \right ), x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 10 \,{\mathrm e}^{t} \sin \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )-4 x \left (t \right )+3 y \left (t \right ) = \sin \left (t \right ), 2 x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = 2 \cos \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )-2 x \left (t \right )-y \left (t \right ) = 2 \,{\mathrm e}^{t}, x \left (t \right )-y^{\prime }\left (t \right )+2 y \left (t \right ) = 3 \,{\mathrm e}^{4 t}]
\] |
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\[
{}[x^{\prime \prime }\left (t \right )+x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 40 \,{\mathrm e}^{3 t}, x^{\prime }\left (t \right )+x \left (t \right )-y^{\prime }\left (t \right ) = 36 \,{\mathrm e}^{t}]
\] |
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\[
{}[x^{\prime }\left (t \right )-2 x \left (t \right )-y \left (t \right ) = 2 \,{\mathrm e}^{t}, y^{\prime }\left (t \right )-2 y \left (t \right )-4 z \left (t \right ) = 4 \,{\mathrm e}^{2 t}, x \left (t \right )-z^{\prime }\left (t \right )-z \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime \prime }\left (t \right )+2 x \left (t \right )-2 y^{\prime }\left (t \right ) = 0, 3 x^{\prime }\left (t \right )+y^{\prime \prime }\left (t \right )-8 y \left (t \right ) = 240 \,{\mathrm e}^{t}]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = 0, x \left (t \right )-y^{\prime }\left (t \right ) = 15 \cos \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = 2 \sin \left (t \right ) \left (1-\operatorname {Heaviside}\left (t -\pi \right )\right ), 2 x \left (t \right )-y^{\prime }\left (t \right )-y \left (t \right ) = 0]
\] |
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\[
{}[2 x^{\prime }\left (t \right )+x \left (t \right )-5 y^{\prime }\left (t \right )-4 y \left (t \right ) = 28 \,{\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right ), 3 x^{\prime }\left (t \right )-2 x \left (t \right )-4 y^{\prime }\left (t \right )+y \left (t \right ) = 0]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+26 \sin \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+8 x_{2} \left (t \right )+9 t, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+3 \,{\mathrm e}^{-t}]
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right )+\frac {{\mathrm e}^{3 t}}{{\mathrm e}^{2 t}+1}\right ]
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-2 x_{2} \left (t \right )+\frac {2}{{\mathrm e}^{t}-1}, x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+3 x_{2} \left (t \right )-\frac {3}{{\mathrm e}^{t}-1}\right ]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+\frac {4}{\sin \left (2 t \right )}\right ]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+27 t, x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+35 \,{\mathrm e}^{t} t^{{3}/{2}}\right ]
\] |
✓ |
✓ |
|
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+6 \,{\mathrm e}^{-t}, x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+12 t, x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right )-2 x_{3} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-6 x_{2} \left (t \right )+5 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )+4 \,{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+4 \sin \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )+{\mathrm e}^{3 t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )+2 \,{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{3} \left (t \right )+24 t, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+y \left (t \right ) = -{\mathrm e}^{t}, x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = {\mathrm e}^{2 t}]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = t, 5 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = t^{2}]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right )+x \left (t \right )+2 y^{\prime }\left (t \right )+7 y \left (t \right ) = {\mathrm e}^{t}+2, -2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{t}-1]
\] |
✓ |
✓ |
|
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\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{-t}-1, x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+3 y \left (t \right ) = {\mathrm e}^{2 t}+1]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = 1+{\mathrm e}^{t}, y^{\prime }\left (t \right )+2 y \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right ) = {\mathrm e}^{t}+2, x^{\prime }\left (t \right )-x \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right ) = 3+{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime \prime }\left (t \right ) = 4 y \left (t \right )+{\mathrm e}^{t}, y^{\prime \prime }\left (t \right ) = 4 x \left (t \right )-{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -\lambda _{1} x \left (t \right ), y^{\prime }\left (t \right ) = \lambda _{1} x \left (t \right )-\lambda _{2} y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-18 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-9 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{-t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+3 t]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 16 x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-18 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-9 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-18 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-9 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|