| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }+2 y = x^{2} {\mathrm e}^{-x}
\]
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{} y^{\prime \prime }-y^{\prime }-2 y = x^{2}-8
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{} y^{\prime \prime }+4 y = x \sin \left (x \right )
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{} y^{\prime \prime }+y = x^{2} \cos \left (x \right )
\]
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{} y^{\prime \prime }-y = x^{2} \cos \left (x \right )
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{} 2 y^{\prime \prime }+3 y^{\prime }-2 y = x^{2} {\mathrm e}^{x}
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = x^{2} \cos \left (x \right )
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{} y^{\prime \prime }-4 y^{\prime }+3 y = x^{2} \sin \left (x \right )
\]
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{} y^{\prime \prime }-y = \sin \left (2 x \right ) x
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{} y^{\prime \prime }+2 y^{\prime } = x^{3} \sin \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }-y^{\prime } = x \,{\mathrm e}^{2 x} \sin \left (x \right )
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{} y^{\prime \prime }-4 y = x \,{\mathrm e}^{2 x} \cos \left (x \right )
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{} y^{\prime \prime }+2 y^{\prime } = x^{2} {\mathrm e}^{-x} \sin \left (x \right )
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| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+y = 0
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{} x^{2} y^{\prime \prime }+x y^{\prime }+16 y = 0
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{} 4 x^{2} y^{\prime \prime }-16 x y^{\prime }+25 y = 0
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{} x^{2} y^{\prime \prime }+5 x y^{\prime }+10 y = 0
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{} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }-18 y = \ln \left (x \right )
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{} 2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = \ln \left (x^{2}\right )
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{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{3}
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{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 1-x
\]
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{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 4 x +\sin \left (\ln \left (x \right )\right )
\]
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{} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x^{2} \ln \left (x \right )
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{} x^{2} y^{\prime \prime }+4 x y^{\prime }+3 y = \left (x -1\right ) \ln \left (x \right )
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{} y^{\prime \prime } = \cos \left (t \right )
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| \[
{} y^{\prime \prime } = k^{2} y
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{} x^{\prime \prime }+k^{2} x = 0
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{} y^{3} y^{\prime \prime }+4 = 0
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| \[
{} x^{\prime \prime } = \frac {k^{2}}{x^{2}}
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| \[
{} x y^{\prime \prime } = x^{2}+1
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| \[
{} \left (1-x \right ) y^{\prime \prime } = y^{\prime }
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (1+y^{\prime }\right ) x = 0
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| \[
{} y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime }
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| \[
{} x y^{\prime \prime }+x = y^{\prime }
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| \[
{} x^{\prime \prime }+t x^{\prime } = t^{3}
\]
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{} x^{2} y^{\prime \prime } = x y^{\prime }+1
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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 } = 1
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{} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
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| \[
{} y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime }
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| \[
{} y^{\prime \prime } = y y^{\prime }
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{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
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{} y^{\prime \prime }+y y^{\prime } = 0
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| \[
{} y^{\prime \prime }+2 {y^{\prime }}^{2} = 0
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{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
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{} y y^{\prime \prime }+1 = {y^{\prime }}^{2}
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| \[
{} y^{\prime \prime } = y
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{} y y^{\prime \prime }+{y^{\prime }}^{2} = y y^{\prime }
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
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| \[
{} y^{\prime \prime }+2 {y^{\prime }}^{2} = 2
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| \[
{} y^{\prime \prime }+y^{\prime } = {y^{\prime }}^{3}
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| \[
{} \left (1+y\right ) y^{\prime \prime } = 3 {y^{\prime }}^{2}
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| \[
{} y^{\prime \prime } = \tan \left (x \right ) \sec \left (x \right )
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{} 2 y^{\prime \prime } = {\mathrm e}^{y}
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{} y^{\prime \prime } = y^{3}
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| \[
{} y^{\prime \prime } = {y^{\prime }}^{2} \cos \left (x \right )
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| \[
{} y y^{\prime \prime }-y^{2} y^{\prime } = {y^{\prime }}^{2}
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{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
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| \[
{} y y^{\prime \prime } = y^{3}+{y^{\prime }}^{2}
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| \[
{} \left (1+{y^{\prime }}^{2}\right )^{2} = y^{2} y^{\prime \prime }
\]
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{} y^{\prime \prime } = {y^{\prime }}^{2} \sin \left (x \right )
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| \[
{} 2 y y^{\prime \prime } = y^{3}+2 {y^{\prime }}^{2}
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| \[
{} x^{\prime \prime }-k^{2} x = 0
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{} y y^{\prime \prime } = 2 {y^{\prime }}^{2}+y^{2}
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| \[
{} \left (-{\mathrm e}^{x}+1\right ) y^{\prime \prime } = {\mathrm e}^{x} y^{\prime }
\]
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime } = 0
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| \[
{} x^{\prime \prime }+\omega _{0}^{2} x = a \cos \left (\omega t \right )
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| \[
{} f^{\prime \prime }+2 f^{\prime }+5 f = 0
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{} f^{\prime \prime }+2 f^{\prime }+5 f = {\mathrm e}^{-t} \cos \left (3 t \right )
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{} f^{\prime \prime }+6 f^{\prime }+9 f = {\mathrm e}^{-t}
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| \[
{} f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t}
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{} f^{\prime \prime }+8 f^{\prime }+12 f = 12 \,{\mathrm e}^{-4 t}
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 4 \,{\mathrm e}^{-x}
\]
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| \[
{} \frac {y^{\prime \prime }}{y}-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y} = 2 a^{2}
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = x
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{} \left (1+x \right )^{2} y^{\prime \prime }+3 y^{\prime } \left (1+x \right )+y = x^{2}
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{} \left (x -2\right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}} = 0
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| \[
{} y^{\prime \prime }-y = x^{n}
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{} y^{\prime \prime }-2 y^{\prime }+y = 2 x \,{\mathrm e}^{x}
\]
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{} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = {\mathrm e}^{-x^{2}} \sin \left (2 x \right )
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| \[
{} y^{\prime \prime }-25 y = 0
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{} y^{\prime \prime }+4 y = 0
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{} y^{\prime \prime }+y^{\prime }-2 y = 0
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 0
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{} y^{\prime \prime }-9 y = 0
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{} x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0
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{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
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{} x^{2} y^{\prime \prime }-3 x y^{\prime }+13 y = 0
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{} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y = 9 x^{2}
\]
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{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{4} \sin \left (x \right )
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{} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+b y a = 0
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| \[
{} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
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| \[
{} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y = 0
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{} y^{\prime \prime }-y^{\prime }-6 y = 0
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{} y^{\prime \prime }+6 y^{\prime }+9 y = 0
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{} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
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{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0
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| \[
{} y^{\prime \prime } = x \,{\mathrm e}^{x}
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{} y^{\prime \prime } = x^{n}
\]
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| \[
{} y^{\prime \prime } = \cos \left (x \right )
\]
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