| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x y^{\prime \prime } = y^{\prime }
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{} x y^{\prime \prime }+y^{\prime } = 0
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{} x y^{\prime \prime } = \left (2 x^{2}+1\right ) y^{\prime }
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{} x y^{\prime \prime } = y^{\prime }+x^{2}
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{} x \ln \left (x \right ) y^{\prime \prime } = y^{\prime }
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{} 2 y^{\prime \prime } = \frac {y^{\prime }}{x}+\frac {x^{2}}{y^{\prime }}
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{} y^{\prime \prime } = \sqrt {1+{y^{\prime }}^{2}}
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{} y^{\prime \prime } = {y^{\prime }}^{2}
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{} y^{\prime \prime } = \sqrt {1-{y^{\prime }}^{2}}
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{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
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{} y^{\prime \prime } = \sqrt {1+y^{\prime }}
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{} y^{\prime \prime } = y^{\prime } \ln \left (y^{\prime }\right )
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| \[
{} y^{\prime \prime }+y^{\prime }+2 = 0
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| \[
{} y^{\prime \prime } = y^{\prime } \left (1+y^{\prime }\right )
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{} 3 y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
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{} y y^{\prime \prime } = {y^{\prime }}^{2}
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| \[
{} y^{\prime \prime } = 2 y y^{\prime }
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{} 3 y^{\prime } y^{\prime \prime } = 2 y
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{} 2 y^{\prime \prime } = 3 y^{2}
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 0
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| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime }
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{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
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{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
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| \[
{} y^{3} y^{\prime \prime } = -1
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{2} y^{\prime }
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{} y^{\prime \prime } = {\mathrm e}^{2 y}
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{} 2 y y^{\prime \prime }-3 {y^{\prime }}^{2} = 4 y^{2}
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{} y^{\prime \prime }-y = 0
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{} 3 y^{\prime \prime }-2 y^{\prime }-8 y = 0
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{} y^{\prime \prime }+2 y^{\prime }+y = 0
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{} y^{\prime \prime }-4 y^{\prime }+3 y = 0
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{} y^{\prime \prime }-2 y^{\prime }-2 y = 0
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{} 4 y^{\prime \prime }-8 y^{\prime }+5 y = 0
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{} y^{\prime \prime }-2 y^{\prime }+2 y = 0
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| \[
{} y^{\prime \prime }-2 y^{\prime }+3 y = 0
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| \[
{} y^{\prime \prime }+3 y^{\prime } = 3
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{} y^{\prime \prime }-7 y^{\prime } = \left (x -1\right )^{2}
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{} y^{\prime \prime }+3 y^{\prime } = {\mathrm e}^{x}
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| \[
{} y^{\prime \prime }+7 y^{\prime } = {\mathrm e}^{-7 x}
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{} y^{\prime \prime }-8 y^{\prime }+16 y = \left (1-x \right ) {\mathrm e}^{4 x}
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{} y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 x}
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{} 4 y^{\prime \prime }-3 y^{\prime } = x \,{\mathrm e}^{\frac {3 x}{4}}
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{} y^{\prime \prime }-4 y^{\prime } = x \,{\mathrm e}^{4 x}
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{} y^{\prime \prime }+25 y = \cos \left (5 x \right )
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{} y^{\prime \prime }+y = \sin \left (x \right )-\cos \left (x \right )
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{} y^{\prime \prime }+16 y = \sin \left (4 x +\alpha \right )
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{} y^{\prime \prime }+4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )+\cos \left (2 x \right )\right )
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{} y^{\prime \prime }-4 y^{\prime }+8 y = {\mathrm e}^{2 x} \left (\sin \left (2 x \right )-\cos \left (2 x \right )\right )
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{} y^{\prime \prime }+6 y^{\prime }+13 y = {\mathrm e}^{-3 x} \cos \left (2 x \right )
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| \[
{} y^{\prime \prime }+k^{2} y = k \sin \left (k x +\alpha \right )
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{} y^{\prime \prime }+k^{2} y = k
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{} y^{\prime \prime }+2 y^{\prime }+y = -2
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| \[
{} y^{\prime \prime }+2 y^{\prime } = -2
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| \[
{} y^{\prime \prime }+9 y = 9
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{} y^{\prime \prime }-4 y^{\prime }+4 y = x^{2}
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| \[
{} y^{\prime \prime }+8 y^{\prime } = 8 x
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{} y^{\prime \prime }-2 k y^{\prime }+k^{2} y = {\mathrm e}^{x}
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{} y^{\prime \prime }+4 y^{\prime }+4 y = 8 \,{\mathrm e}^{-2 x}
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{} y^{\prime \prime }+4 y^{\prime }+3 y = 9 \,{\mathrm e}^{-3 x}
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| \[
{} 7 y^{\prime \prime }-y^{\prime } = 14 x
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{} y^{\prime \prime }+3 y^{\prime } = 3 x \,{\mathrm e}^{-3 x}
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{} y^{\prime \prime }+5 y^{\prime }+6 y = 10 \left (1-x \right ) {\mathrm e}^{-2 x}
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{} y^{\prime \prime }+2 y^{\prime }+2 y = 1+x
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{} y^{\prime \prime }+y^{\prime }+y = \left (x^{2}+x \right ) {\mathrm e}^{x}
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{} y^{\prime \prime }+4 y^{\prime }-2 y = 8 \sin \left (2 x \right )
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{} y^{\prime \prime }+y = 4 x \cos \left (x \right )
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{} y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \sin \left (n x \right )
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{} y^{\prime \prime }+2 y^{\prime }+5 y = \sin \left (2 x \right ) {\mathrm e}^{-x}
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{} y^{\prime \prime }+a^{2} y = 2 \cos \left (m x \right )+3 \sin \left (m x \right )
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{} y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )
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{} y^{\prime \prime }+2 y^{\prime } = 4 \,{\mathrm e}^{x} \left (\cos \left (x \right )+\sin \left (x \right )\right )
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{} 5 y+4 y^{\prime }+y^{\prime \prime } = 10 \,{\mathrm e}^{-2 x} \cos \left (x \right )
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{} 4 y^{\prime \prime }+8 y^{\prime } = x \sin \left (x \right )
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{} y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{x}
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{} y^{\prime \prime }+y^{\prime }-2 y = x^{2} {\mathrm e}^{4 x}
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \left (x^{2}+x \right ) {\mathrm e}^{3 x}
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{} y^{\prime \prime }-2 y^{\prime }+y = x^{3}
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{} y^{\prime \prime }+y = x^{2} \sin \left (x \right )
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{} y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \cos \left (x \right )
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{} y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right )
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{} y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{x}+{\mathrm e}^{-2 x}
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{} y^{\prime \prime }+4 y^{\prime } = x +{\mathrm e}^{-4 x}
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{} y^{\prime \prime }-y = x +\sin \left (x \right )
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{} y^{\prime \prime }-2 y^{\prime }+2 y = \left (\sin \left (x \right )+1\right ) {\mathrm e}^{x}
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{} y^{\prime \prime }+4 y = \sin \left (2 x \right ) \sin \left (x \right )
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{} y^{\prime \prime }-4 y^{\prime } = 2 \cos \left (4 x \right )^{2}
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{} y^{\prime \prime }-y^{\prime }-2 y = 4 x -2 \,{\mathrm e}^{x}
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{} y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right )
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{} y^{\prime \prime }-2 y^{\prime }+y = 2+{\mathrm e}^{x} \sin \left (x \right )
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{} y^{\prime \prime }+2 y^{\prime }+2 y = \left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x}
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right )
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{} 2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right )
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{} y^{\prime \prime }+4 y = x \sin \left (x \right )^{2}
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{} y^{\prime \prime }+y^{\prime } = \cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2}
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{} y^{\prime \prime }-2 y^{\prime }+5 y = 10 \sin \left (x \right )+17 \sin \left (2 x \right )
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{} y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x}
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{} y^{\prime \prime }-2 y^{\prime }-3 y = 2 x +{\mathrm e}^{-x}-2 \,{\mathrm e}^{3 x}
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{} y^{\prime \prime }+4 y = {\mathrm e}^{x}+4 \sin \left (2 x \right )+2 \cos \left (x \right )^{2}-1
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{} y^{\prime \prime }+3 y^{\prime }+2 y = 6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right )
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{} y^{\prime \prime }+y = \cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2}
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