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ODE |
Mathematica |
Maple |
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\[
{}x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\] |
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\[
{}x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\] |
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\[
{}x^{\prime \prime }+\left (x^{2}+1\right ) x^{\prime }+x^{3} = 0
\] |
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\[
{}t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (2+t \right ) y = 0
\] |
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\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
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\[
{}\left (\cos \left (t \right ) t -\sin \left (t \right )\right ) x^{\prime \prime }-x^{\prime } t \sin \left (t \right )-x \sin \left (t \right ) = 0
\] |
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\[
{}\left (-t^{2}+t \right ) x^{\prime \prime }+\left (-t^{2}+2\right ) x^{\prime }+\left (2-t \right ) x = 0
\] |
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\[
{}y^{\prime \prime }-x y^{\prime }+y = 0
\] |
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\[
{}\tan \left (t \right ) x^{\prime \prime }-3 x^{\prime }+\left (\tan \left (t \right )+3 \cot \left (t \right )\right ) x = 0
\] |
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\[
{}t^{2} x^{\prime \prime }-2 x = t^{3}
\] |
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\[
{}\left (\tan \left (x \right )^{2}-1\right ) y^{\prime \prime }-4 \tan \left (x \right )^{3} y^{\prime }+2 y \sec \left (x \right )^{4} = \left (\tan \left (x \right )^{2}-1\right ) \left (1-2 \sin \left (x \right )^{2}\right )
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
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\[
{}t^{2} x^{\prime \prime }-5 t x^{\prime }+10 x = 0
\] |
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\[
{}t^{2} x^{\prime \prime }+t x^{\prime }-x = 0
\] |
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\[
{}x^{2} z^{\prime \prime }+3 x z^{\prime }+4 z = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 0
\] |
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\[
{}4 t^{2} x^{\prime \prime }+8 t x^{\prime }+5 x = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+5 y = 0
\] |
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\[
{}3 x^{2} z^{\prime \prime }+5 x z^{\prime }-z = 0
\] |
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\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+13 x = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 2
\] |
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\[
{}y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
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\[
{}x^{3} x^{\prime \prime }+1 = 0
\] |
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\[
{}{y^{\prime \prime \prime }}^{2}+{y^{\prime \prime }}^{2} = 1
\] |
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\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-\frac {1}{25}\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+{y^{\prime }}^{2} = 1
\] |
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\[
{}y^{\prime \prime } = 3 \sqrt {y}
\] |
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\[
{}u^{\prime \prime }+\frac {2 u^{\prime }}{r} = 0
\] |
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\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = \frac {y y^{\prime }}{\sqrt {x^{2}+1}}
\] |
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\[
{}y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}+{y^{\prime \prime }}^{2}
\] |
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\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y = 1
\] |
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\[
{}m x^{\prime \prime } = f \left (x\right )
\] |
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\[
{}m x^{\prime \prime } = f \left (x^{\prime }\right )
\] |
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\[
{}\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 2 \cos \left (\ln \left (1+x \right )\right )
\] |
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\[
{}x^{3} y^{\prime \prime }-x y^{\prime }+y = 0
\] |
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\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
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\[
{}6 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0
\] |
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\[
{}x y^{\prime \prime } = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right )
\] |
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\[
{}y^{\prime \prime } = 2 y^{3}
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\] |
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\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
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\[
{}y^{\prime \prime \prime }+x y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y y^{\prime } = 1
\] |
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\[
{}y^{\prime \prime }+y y^{\prime \prime \prime \prime } = 1
\] |
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\[
{}y^{\prime \prime \prime }+x y = \cosh \left (x \right )
\] |
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\[
{}y^{\prime \prime \prime }+x y = \cosh \left (x \right )
\] |
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\[
{}2 y^{\prime \prime }+3 y^{\prime }+4 x^{2} y = 1
\] |
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\[
{}x^{2} y^{\prime \prime }-y = \sin \left (x \right )^{2}
\] |
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\[
{}y^{\prime \prime \prime }+x y^{\prime \prime }-y^{2} = \sin \left (x \right )
\] |
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\[
{}\sin \left (y^{\prime \prime }\right )+y y^{\prime \prime \prime \prime } = 1
\] |
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\[
{}\sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = x y
\] |
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\[
{}y y^{\prime \prime } = 1
\] |
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\[
{}{y^{\prime \prime \prime }}^{2}+\sqrt {y} = \sin \left (x \right )
\] |
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\[
{}\left (x -3\right ) y^{\prime \prime }+y \ln \left (x \right ) = x^{2}
\] |
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\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cot \left (x \right ) = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
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\[
{}x y^{\prime \prime }+2 x^{2} y^{\prime }+y \sin \left (x \right ) = \sinh \left (x \right )
\] |
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\[
{}\sin \left (x \right ) y^{\prime \prime }+x y^{\prime }+7 y = 1
\] |
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\[
{}y^{\prime \prime }-\left (x -1\right ) y^{\prime }+x^{2} y = \tan \left (x \right )
\] |
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\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x^{2} y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {k x}{y^{4}} = 0
\] |
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\[
{}y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\] |
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\[
{}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+2 x^{2} y^{\prime }+4 x y = 2 x
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 1-2 x
\] |
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\[
{}y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+2 \left (1-x \right ) y = 0
\] |
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\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 2 x
\] |
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\[
{}\ln \left (x^{2}+1\right ) y^{\prime \prime }+\frac {4 x y^{\prime }}{x^{2}+1}+\frac {\left (-x^{2}+1\right ) y}{\left (x^{2}+1\right )^{2}} = 0
\] |
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\[
{}x y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
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\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = \cos \left (x \right )
\] |
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\[
{}y^{\prime \prime }+\cot \left (x \right ) y^{\prime }-\csc \left (x \right )^{2} y = \cos \left (x \right )
\] |
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\[
{}x \ln \left (x \right ) y^{\prime \prime }+2 y^{\prime }-\frac {y}{x} = 1
\] |
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\[
{}x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0
\] |
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\[
{}\frac {x y^{\prime \prime }}{1+y}+\frac {y y^{\prime }-x {y^{\prime }}^{2}+y^{\prime }}{\left (1+y\right )^{2}} = x \sin \left (x \right )
\] |
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\[
{}\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime \prime }-x {y^{\prime }}^{2} \sin \left (y\right )+2 \left (\cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime } = y \sin \left (x \right )
\] |
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\[
{}y y^{\prime \prime } \sin \left (x \right )+\left (\sin \left (x \right ) y^{\prime }+y \cos \left (x \right )\right ) y^{\prime } = \cos \left (x \right )
\] |
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\[
{}\left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2} = 0
\] |
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\[
{}\left (\cos \left (y\right )-y \sin \left (y\right )\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right ) = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+\frac {2 x y^{\prime }}{2 x -1}-\frac {4 x y}{\left (2 x -1\right )^{2}} = 0
\] |
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\[
{}\left (x^{2}+2 x \right ) y^{\prime \prime }+\left (x^{2}+x +10\right ) y^{\prime } = \left (25-6 x \right ) y
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{1+x}-\frac {\left (x +2\right ) y}{x^{2} \left (1+x \right )} = 0
\] |
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\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x^{2}+4 x -3\right ) y^{\prime }+8 x y = 0
\] |
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\[
{}\frac {\left (x^{2}-x \right ) y^{\prime \prime }}{x}+\frac {\left (1+3 x \right ) y^{\prime }}{x}+\frac {y}{x} = 3 x
\] |
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\[
{}\left (2 \sin \left (x \right )-\cos \left (x \right )\right ) y^{\prime \prime }+\left (7 \sin \left (x \right )+4 \cos \left (x \right )\right ) y^{\prime }+10 y \cos \left (x \right ) = 0
\] |
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\[
{}y^{\prime \prime }+\frac {\left (x -1\right ) y^{\prime }}{x}+\frac {y}{x^{3}} = \frac {{\mathrm e}^{-\frac {1}{x}}}{x^{3}}
\] |
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\[
{}y^{\prime \prime }+\left (2 x +5\right ) y^{\prime }+\left (4 x +8\right ) y = {\mathrm e}^{-2 x}
\] |
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\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = t^{7}
\] |
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\[
{}t^{2} y^{\prime \prime }-6 t y^{\prime }+\sin \left (2 t \right ) y = \ln \left (t \right )
\] |
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\[
{}y^{\prime \prime }+3 y^{\prime }+\frac {y}{t} = t
\] |
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\[
{}y^{\prime \prime }+t y^{\prime }-y \ln \left (t \right ) = \cos \left (2 t \right )
\] |
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\[
{}t^{3} y^{\prime \prime }-2 t y^{\prime }+y = t^{4}
\] |
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\[
{}\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{4 x^{2}}\right ) y = x
\] |
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\[
{}x^{2} y^{\prime \prime }+x \left (x -\frac {1}{2}\right ) y^{\prime }+\frac {y}{2} = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-y = 0
\] |
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