| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\]
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{} x^{\prime \prime }+4 x = \sin \left (2 t \right )^{2}
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{} t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = t \ln \left (t \right )
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{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x^{5}}
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{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{3 x}
\]
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| \[
{} y^{\prime \prime }-60 y^{\prime }-900 y = 5 \,{\mathrm e}^{10 x}
\]
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| \[
{} y^{\prime \prime }-7 y^{\prime } = -3
\]
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{} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right )
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{} x^{2} y^{\prime \prime }-x y^{\prime } = x^{3} {\mathrm e}^{x}
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| \[
{} y^{\prime \prime }-y = 0
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{} y^{\prime \prime }-y = \sin \left (x \right )
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{} y^{\prime \prime }-y = {\mathrm e}^{x}
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{} y^{\prime \prime }+2 y^{\prime }-3 y = \sin \left (2 x \right )
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{} y^{\prime \prime }+y = \sin \left (x \right )
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| \[
{} y^{\prime \prime }+y^{\prime }+y = 0
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 3 \,{\mathrm e}^{-2 x}
\]
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{} y^{\prime \prime }+5 y^{\prime }-3 y = \operatorname {Heaviside}\left (x -4\right )
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| \[
{} x^{\prime \prime }+4 x^{\prime }+4 x = 0
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{} q^{\prime \prime }+9 q^{\prime }+14 q = \frac {\sin \left (t \right )}{2}
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{} y^{\prime \prime }-2 y^{\prime }+y = 0
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{} \left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
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{} y^{\prime \prime }-y = 0
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| \[
{} y^{\prime \prime }-y = 4-x
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 0
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{} y^{\prime \prime }-3 y^{\prime }+2 y = 2 \left (1-x \right ) {\mathrm e}^{x}
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{} y^{\prime \prime }+y^{\prime }-6 y = 0
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{5 x}
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{} y^{\prime \prime }+9 y = x \cos \left (x \right )
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{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
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{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
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{} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 2
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| \[
{} {y^{\prime }}^{3}+y y^{\prime \prime } = 0
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| \[
{} y^{\prime \prime }+2 y^{\prime }-15 y = 0
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{} y^{\prime \prime }+6 y^{\prime }+9 y = 0
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{} y^{\prime \prime }-4 y^{\prime }+13 y = 0
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{} y^{\prime \prime }+25 y = 0
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{} y^{\prime \prime }-4 y^{\prime }+3 y = 1
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| \[
{} y^{\prime \prime }-4 y^{\prime } = 5
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{} y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{2 x}
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{} y^{\prime \prime }+y^{\prime }-2 y = -2 x^{2}+2 x +2
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{} y^{\prime \prime }-y = 4 x \,{\mathrm e}^{x}
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{} y^{\prime \prime }-y = \sin \left (x \right )^{2}
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{} y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
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{} y^{\prime \prime }+y = \csc \left (x \right )
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right )
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{} y^{\prime \prime }+y = \csc \left (x \right )
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{} y^{\prime \prime }+4 y = 4 \sec \left (x \right )^{2}
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{} y^{\prime \prime }-4 y^{\prime }+3 y = \frac {1}{1+{\mathrm e}^{-x}}
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| \[
{} y^{\prime \prime }-y = {\mathrm e}^{-x} \sin \left ({\mathrm e}^{-x}\right )+\cos \left ({\mathrm e}^{-x}\right )
\]
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{} y^{\prime \prime }-y = \frac {1}{\left (1+{\mathrm e}^{-x}\right )^{2}}
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{} y^{\prime \prime }+2 y = {\mathrm e}^{x}+2
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{} y^{\prime \prime }-y = \sin \left (2 x \right ) {\mathrm e}^{x}
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{} y^{\prime \prime }+2 y^{\prime }+2 y = x^{2}+\sin \left (x \right )
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{} y^{\prime \prime }-9 y = x +{\mathrm e}^{2 x}-\sin \left (2 x \right )
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{} y^{\prime \prime }+y = -2 \sin \left (x \right )+4 x \cos \left (x \right )
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| \[
{} y^{\prime \prime }+y^{\prime }+y = {\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5
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| \[
{} y^{\prime \prime }-y = {\mathrm e}^{x}
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{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{x}+x \,{\mathrm e}^{2 x}
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{} y^{\prime \prime }+4 y = \sin \left (2 x \right )
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{} y^{\prime \prime }+5 y = \cos \left (x \sqrt {5}\right )
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{} y^{\prime \prime }-y = x^{2}
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| \[
{} y^{\prime \prime }+2 y = x^{3}+x^{2}+{\mathrm e}^{-2 x}+\cos \left (3 x \right )
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{} y^{\prime \prime }-2 y^{\prime }-y = {\mathrm e}^{x} \cos \left (x \right )
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{} y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 x}}{x^{2}}
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{} y^{\prime \prime }-y = x \,{\mathrm e}^{3 x}
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{} y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right )
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{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x +x^{2} \ln \left (x \right )
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{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right )
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{} \left (1+x \right )^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right )-y = \ln \left (1+x \right )^{2}+x -1
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| \[
{} -12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime } = 6 x
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{} x y^{\prime \prime }-\left (x +2\right ) y^{\prime }+2 y = 0
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{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 2
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{} \left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 8
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{} \left (1+x \right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (x +2\right ) y = \left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x}
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{} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y = 0
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{} x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y = \left (-x^{2}+6\right ) {\mathrm e}^{x}
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| \[
{} 4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right )^{2} y = 0
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{} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = \left (x^{2}-x +1\right ) {\mathrm e}^{x}
\]
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{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
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{} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}}
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| \[
{} \left (x \sin \left (x \right )+\cos \left (x \right )\right ) y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+y \cos \left (x \right ) = x
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{} x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x} = x +2
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{} \left (1+x \right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y = \left (2+3 x \right ) {\mathrm e}^{3 x}
\]
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{} x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (9 x^{2}+6\right ) y = 0
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{} x y^{\prime \prime }+2 y^{\prime }+4 x y = 4
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{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = \frac {-x^{2}+1}{x}
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{} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
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{} \left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = \frac {2}{x^{3}}
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{} x y^{\prime \prime }-y^{\prime } = -\frac {2}{x}-\ln \left (x \right )
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{} {y^{\prime }}^{3}+y y^{\prime \prime } = 0
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{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
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| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-\cos \left (y\right ) y^{\prime }+y y^{\prime } \sin \left (y\right )\right )
\]
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{} y y^{\prime \prime }-{y^{\prime }}^{2} = \ln \left (y\right ) y^{2}
\]
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{} \left (2 y+x \right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+2 y^{\prime } = 2
\]
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{} 2 \left (1+y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+y^{2}+2 y = 0
\]
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{} \left (1-x \right ) y^{\prime \prime }-4 x y^{\prime }+5 y = \cos \left (x \right )
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| \[
{} u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right )
\]
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| \[
{} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
\]
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