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ODE |
Mathematica |
Maple |
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\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = x^{2}-x -1
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0
\] |
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\[
{}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2}
\] |
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\[
{}\sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 y \sin \left (x \right ) = {\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-\left (a^{2}+1\right ) y = 0
\] |
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\[
{}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
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\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 2 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+y \,{\mathrm e}^{2 x} = {\mathrm e}^{4 x}
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0
\] |
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\[
{}y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y = 0
\] |
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\[
{}x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y = \frac {1}{x^{2}}
\] |
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\[
{}x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-8 x^{3} y = 4 x^{3} {\mathrm e}^{-x^{2}}
\] |
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\[
{}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+3 y = 0
\] |
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\[
{}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (-x^{2}+2\right ) y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
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\[
{}x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y = 0
\] |
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\[
{}\left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 x y = 0
\] |
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\[
{}x^{2} y^{\prime \prime }-2 x \left (1+x \right ) y^{\prime }+2 \left (1+x \right ) y = x^{3}
\] |
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\[
{}x^{2} y^{\prime \prime }-2 n x \left (1+x \right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y = 0
\] |
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\[
{}x^{4} y^{\prime \prime }+2 x^{3} \left (1+x \right ) y^{\prime }+n^{2} y = 0
\] |
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\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\] |
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\[
{}y^{\prime \prime }+x y^{\prime } = x
\] |
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\[
{}y^{\prime \prime } = x \,{\mathrm e}^{x}
\] |
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\[
{}\left (y^{\prime }-x y^{\prime \prime }\right )^{2} = 1+{y^{\prime \prime }}^{2}
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}-y^{\prime } y^{2} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}2 y^{\prime \prime } = {\mathrm e}^{y}
\] |
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\[
{}y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2} = 0
\] |
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\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x
\] |
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\[
{}\left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y = \cos \left (x \right )
\] |
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\[
{}x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y = 0
\] |
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\[
{}x^{2} \left (-x^{3}+1\right ) y^{\prime \prime }-x^{3} y^{\prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2} = 0
\] |
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\[
{}x^{2} y y^{\prime \prime }+\left (x y^{\prime }-y\right )^{2} = 0
\] |
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\[
{}x^{3} y^{\prime \prime }-\left (x y^{\prime }-y\right )^{2} = 0
\] |
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\[
{}y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} \ln \left (y\right )-x^{2} y^{2}
\] |
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\[
{}\sin \left (x \right )^{2} y^{\prime \prime }-2 y = 0
\] |
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\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime } = 2
\] |
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\[
{}y^{\prime \prime }+y y^{\prime } = 0
\] |
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\[
{}\left (x^{2}-x \right ) y^{\prime \prime }+\left (4 x +2\right ) y^{\prime }+2 y = 0
\] |
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\[
{}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\] |
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\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 0
\] |
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\[
{}x \left (x +2 y\right ) y^{\prime \prime }+2 x {y^{\prime }}^{2}+4 \left (x +y\right ) y^{\prime }+2 y+x^{2} = 0
\] |
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\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
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\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2} = 0
\] |
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\[
{}\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right ) = 0
\] |
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\[
{}x^{\prime \prime }+2 x^{\prime }+2 x = 0
\] |
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\[
{}t^{2} x^{\prime \prime }-6 x = 0
\] |
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\[
{}2 x^{\prime \prime }-5 x^{\prime }-3 x = 0
\] |
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\[
{}x^{\prime \prime } = -3 \sqrt {t}
\] |
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\[
{}x^{\prime }+t x^{\prime \prime } = 1
\] |
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\[
{}\frac {x^{\prime }+t x^{\prime \prime }}{t} = -2
\] |
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\[
{}x^{\prime \prime }+x^{\prime } = 3 t
\] |
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\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
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\[
{}x^{\prime \prime }-2 x^{\prime } = 0
\] |
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\[
{}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\] |
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\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
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\[
{}x^{\prime \prime }-4 x^{\prime }+4 x = 0
\] |
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\[
{}x^{\prime \prime }-2 x^{\prime } = 0
\] |
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\[
{}\frac {x^{\prime \prime }}{2}+x^{\prime }+\frac {x}{2} = 0
\] |
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\[
{}x^{\prime \prime }+4 x^{\prime }+3 x = 0
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+4 x = 0
\] |
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\[
{}x^{\prime \prime }-4 x^{\prime }+6 x = 0
\] |
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\[
{}x^{\prime \prime }+9 x = 0
\] |
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\[
{}x^{\prime \prime }-12 x = 0
\] |
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\[
{}2 x^{\prime \prime }+3 x^{\prime }+3 x = 0
\] |
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\[
{}\frac {x^{\prime \prime }}{2}+\frac {5 x^{\prime }}{6}+\frac {2 x}{9} = 0
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = 0
\] |
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\[
{}x^{\prime \prime }+\frac {x^{\prime }}{8}+x = 0
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = 3 t^{3}-1
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = 3 \cos \left (t \right )-2 \sin \left (t \right )
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = 12
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = t^{2} {\mathrm e}^{3 t}
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (7 t \right )
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = {\mathrm e}^{2 t} \cos \left (t \right )+t^{2}
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = t \,{\mathrm e}^{-t} \sin \left (\pi t \right )
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = \left (2+t \right ) \sin \left (\pi t \right )
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = 4 t +5 \,{\mathrm e}^{-t}
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = 5 \sin \left (2 t \right )+t \,{\mathrm e}^{t}
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = t^{3}+1-4 \cos \left (t \right ) t
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+x = -6+2 \,{\mathrm e}^{2 t} \sin \left (t \right )
\] |
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\[
{}x^{\prime \prime }+7 x = t \,{\mathrm e}^{3 t}
\] |
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\[
{}x^{\prime \prime }-x^{\prime } = 6+{\mathrm e}^{2 t}
\] |
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\[
{}x^{\prime \prime }+x = t^{2}
\] |
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\[
{}x^{\prime \prime }-3 x^{\prime }-4 x = 2 t^{2}
\] |
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\[
{}x^{\prime \prime }+x = 9 \,{\mathrm e}^{-t}
\] |
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\[
{}x^{\prime \prime }-4 x = \cos \left (2 t \right )
\] |
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\[
{}x^{\prime \prime }+x^{\prime }+2 x = t \sin \left (2 t \right )
\] |
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\[
{}x^{\prime \prime }-b x^{\prime }+x = \sin \left (2 t \right )
\] |
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\[
{}x^{\prime \prime }-3 x^{\prime }-40 x = 2 \,{\mathrm e}^{-t}
\] |
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\[
{}x^{\prime \prime }-2 x^{\prime } = 4
\] |
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\[
{}x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right )
\] |
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\[
{}x^{\prime \prime }+\frac {x^{\prime }}{100}+4 x = \cos \left (2 t \right )
\] |
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\[
{}x^{\prime \prime }+w^{2} x = \cos \left (\beta t \right )
\] |
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\[
{}x^{\prime \prime }+3025 x = \cos \left (45 t \right )
\] |
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\[
{}x^{\prime \prime } = -\frac {x}{t^{2}}
\] |
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\[
{}x^{\prime \prime } = \frac {4 x}{t^{2}}
\] |
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