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ODE |
Mathematica |
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\[
{}y^{\prime \prime }-4 y = x \,{\mathrm e}^{x}
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5}
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4}
\] |
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\[
{}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{{4}/{3}}
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right )
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1
\] |
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\[
{}x^{\prime \prime }+9 x = 10 \cos \left (2 t \right )
\] |
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\[
{}x^{\prime \prime }+4 x = 5 \sin \left (3 t \right )
\] |
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\[
{}x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right )
\] |
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\[
{}x^{\prime \prime }+25 x = 90 \cos \left (4 t \right )
\] |
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\[
{}m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right )
\] |
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\[
{}x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right )
\] |
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\[
{}x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right )
\] |
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\[
{}2 x^{\prime \prime }+2 x^{\prime }+x = 3 \sin \left (10 t \right )
\] |
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\[
{}x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right )
\] |
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\[
{}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right )
\] |
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\[
{}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right )
\] |
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\[
{}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right )
\] |
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\[
{}x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right )
\] |
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\[
{}x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right )
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right )+3 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right )-t^{2}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right )+x \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{3} \left (t \right )+x_{4} \left (t \right )+t, x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{4} \left (t \right )+t^{2}, x_{4}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+t^{3}]
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0
\] |
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\[
{}4 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
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\[
{}\left (1+x \right ) y^{\prime \prime }-\left (x +2\right ) y^{\prime }+y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
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\[
{}5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime } = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime } = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 0
\] |
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\[
{}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-16 y^{\prime \prime }+16 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0
\] |
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\[
{}6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime } = 16 y
\] |
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\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
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\[
{}2 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime } = 0
\] |
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\[
{}3 y^{\prime \prime \prime }+2 y^{\prime \prime } = 0
\] |
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\[
{}y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime } = 0
\] |
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\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 0
\] |
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\[
{}2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime \prime }+27 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y = 0
\] |
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\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y = 0
\] |
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\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y = 0
\] |
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\[
{}y^{\prime \prime \prime } = y
\] |
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\[
{}y^{\prime \prime \prime \prime } = y^{\prime \prime \prime }+y^{\prime \prime }+y^{\prime }+2 y
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime } = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+x y^{\prime } = 0
\] |
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\[
{}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-7 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )+5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
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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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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -50 x_{1} \left (t \right )+20 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 100 x_{1} \left (t \right )-60 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+7 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )+5 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-6 x_{2} \left (t \right )-5 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+5 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )+4 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 4 x_{3} \left (t \right )+4 x_{4} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+9 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-10 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{3} \left (t \right )+8 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{4} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -21 x_{1} \left (t \right )-5 x_{2} \left (t \right )-27 x_{3} \left (t \right )-9 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -21 x_{3} \left (t \right )-2 x_{4} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+7 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right )+10 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+10 x_{2} \left (t \right )+4 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+4 x_{4} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -40 x_{1} \left (t \right )-12 x_{2} \left (t \right )+54 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 35 x_{1} \left (t \right )+13 x_{2} \left (t \right )-46 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -25 x_{1} \left (t \right )-7 x_{2} \left (t \right )+34 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -20 x_{1} \left (t \right )+11 x_{2} \left (t \right )+13 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 12 x_{1} \left (t \right )-x_{2} \left (t \right )-7 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -48 x_{1} \left (t \right )+21 x_{2} \left (t \right )+31 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 147 x_{1} \left (t \right )+23 x_{2} \left (t \right )-202 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -90 x_{1} \left (t \right )-9 x_{2} \left (t \right )+129 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 90 x_{1} \left (t \right )+15 x_{2} \left (t \right )-123 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )-7 x_{2} \left (t \right )-5 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -12 x_{1} \left (t \right )+7 x_{2} \left (t \right )+11 x_{3} \left (t \right )+9 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 24 x_{1} \left (t \right )-17 x_{2} \left (t \right )-19 x_{3} \left (t \right )-9 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -18 x_{1} \left (t \right )+13 x_{2} \left (t \right )+17 x_{3} \left (t \right )+9 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 13 x_{1} \left (t \right )-42 x_{2} \left (t \right )+106 x_{3} \left (t \right )+139 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-16 x_{2} \left (t \right )+52 x_{3} \left (t \right )+70 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+6 x_{2} \left (t \right )-20 x_{3} \left (t \right )-31 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-6 x_{2} \left (t \right )+22 x_{3} \left (t \right )+33 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 23 x_{1} \left (t \right )-18 x_{2} \left (t \right )-16 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )+6 x_{2} \left (t \right )+7 x_{3} \left (t \right )+9 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 34 x_{1} \left (t \right )-27 x_{2} \left (t \right )-26 x_{3} \left (t \right )-9 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -26 x_{1} \left (t \right )+21 x_{2} \left (t \right )+25 x_{3} \left (t \right )+12 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|