| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y = 0
\]
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| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 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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| \[
{} x^{\prime \prime }-3 x^{\prime }+2 x = 6 \,{\mathrm e}^{3 t}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 10
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 5+10 \sin \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 3 \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+5 y^{\prime }-6 y = 3 \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+y = \sec \left (x \right )^{3}
\]
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| \[
{} y^{\prime \prime }+y^{\prime } = 3 x^{2}
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| \[
{} y^{\prime \prime }-y = {\mathrm e}^{x}+1
\]
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| \[
{} y^{\prime \prime }+y = \tan \left (x \right )
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| \[
{} y^{\prime \prime }-4 y^{\prime }+4 y = 6 x \,{\mathrm e}^{2 x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}}
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{} y^{\prime \prime }-3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{x}\right )
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y = 0
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y = 0
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| \[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+3 y = 0
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 0
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| \[
{} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0
\]
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| \[
{} 4 x^{2} y^{\prime \prime }+y = 0
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-3 y = 3 x^{2}
\]
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| \[
{} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = x^{2}+x
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| \[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 2 x^{3}
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+3 y = 5 x^{2}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 20 \,{\mathrm e}^{-2 x}
\]
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| \[
{} y^{\prime \prime }+y = 2 \sin \left (3 x \right )
\]
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| \[
{} y^{\prime \prime }+y = 1+2 \cos \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 3 x^{2}-x
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| \[
{} x^{\prime \prime }+x = 5 t^{2}
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| \[
{} x^{\prime \prime }+x = 2 \tan \left (t \right )
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| \[
{} y^{\prime \prime }-k^{2} y = f \left (x \right )
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| \[
{} y^{\prime \prime }-y = {\mathrm e}^{-x}
\]
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| \[
{} y^{\prime \prime }-4 y = {\mathrm e}^{2 x}
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-15 y = x^{4} {\mathrm e}^{x}
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = 0
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| \[
{} y^{\prime \prime }+2 y^{\prime }+5 y = 0
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| \[
{} y^{\prime \prime }-y = t \,{\mathrm e}^{2 t}
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| \[
{} y^{\prime \prime }-3 y^{\prime }-4 y = t^{2}
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| \[
{} y^{\prime \prime }-3 y^{\prime }-2 y = {\mathrm e}^{t}
\]
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| \[
{} y^{\prime \prime }+4 y = \delta \left (t -1\right )
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{} y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -1\right )
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| \[
{} y^{\prime \prime }+6 y^{\prime }+18 y = 2 \operatorname {Heaviside}\left (\pi -t \right )
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x}
\]
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| \[
{} u^{\prime \prime }+2 a u^{\prime }+\omega ^{2} u = c \cos \left (\omega t \right )
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| \[
{} z^{2} u^{\prime \prime }+\left (3 z +1\right ) u^{\prime }+u = 0
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| \[
{} x^{\prime \prime }+x = 0
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| \[
{} x^{\prime \prime }+4 x = 0
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| \[
{} x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x = 0
\]
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| \[
{} x^{\prime \prime }+\frac {x^{\prime }}{t}+q \left (t \right ) x = 0
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| \[
{} 2 x^{\prime \prime }+x^{\prime }-x = 0
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| \[
{} x^{\prime \prime }+2 x^{\prime }+2 x = 0
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| \[
{} x^{\prime \prime }+8 x^{\prime }+16 x = 0
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| \[
{} x^{\prime \prime }+2 x^{\prime }-15 x = 0
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| \[
{} x^{\prime \prime }-3 x^{\prime }+2 x = 0
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| \[
{} 4 x^{\prime }+2 x^{\prime \prime } = -5 x
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| \[
{} x^{\prime \prime }-6 x^{\prime }+9 x = 0
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| \[
{} x^{\prime \prime }+x^{\prime }-\beta x = 0
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| \[
{} x^{\prime \prime }+4 x^{\prime }+k x = 0
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| \[
{} x^{\prime \prime }+b x^{\prime }+c x = 0
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| \[
{} x^{\prime \prime }+5 x^{\prime }+6 x = 0
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| \[
{} x^{\prime \prime }+p x^{\prime } = 0
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| \[
{} x^{\prime \prime }+x^{\prime }-2 x = 0
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| \[
{} x^{\prime \prime }-2 x^{\prime }+2 x = 0
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| \[
{} x^{\prime \prime }-2 a x^{\prime }+b x = 0
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| \[
{} x^{\prime \prime }+\lambda ^{2} x = 0
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| \[
{} x^{\prime \prime }+x = 0
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| \[
{} x^{\prime \prime }-x = 0
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| \[
{} x^{\prime \prime }+x^{\prime }-2 x = 0
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| \[
{} x^{\prime \prime }-2 x^{\prime }+5 x = 0
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| \[
{} x^{\prime \prime }-2 x^{\prime }+5 x = 0
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| \[
{} x^{\prime \prime }+2 x^{\prime } = 0
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| \[
{} x^{\prime \prime }-4 x = t
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| \[
{} x^{\prime \prime }-4 x = 4 t^{2}
\]
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| \[
{} x^{\prime \prime }+x = t^{2}-2 t
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| \[
{} x^{\prime \prime }+x = 3 t^{2}+t
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| \[
{} x^{\prime \prime }-x = {\mathrm e}^{-3 t}
\]
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| \[
{} x^{\prime \prime }-x = 3 \,{\mathrm e}^{2 t}
\]
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| \[
{} x^{\prime \prime }-x = t \,{\mathrm e}^{2 t}
\]
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| \[
{} x^{\prime \prime }-3 x^{\prime }-x = t^{2}+t
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| \[
{} x^{\prime \prime }-4 x^{\prime }+13 x = 20 \,{\mathrm e}^{t}
\]
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| \[
{} x^{\prime \prime }-x^{\prime }-2 x = 2 t +{\mathrm e}^{t}
\]
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{} x^{\prime \prime }+4 x = \cos \left (t \right )
\]
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{} x^{\prime \prime }+x = \sin \left (2 t \right )-\cos \left (3 t \right )
\]
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| \[
{} x^{\prime \prime }+2 x^{\prime }+2 x = \cos \left (2 t \right )
\]
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{} x^{\prime \prime }+x = t \sin \left (2 t \right )
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| \[
{} x^{\prime \prime }-x^{\prime } = t
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{} x^{\prime \prime }-x = {\mathrm e}^{k t}
\]
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{} x^{\prime \prime }-x^{\prime }-2 x = 3 \,{\mathrm e}^{-t}
\]
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{} x^{\prime \prime }-3 x^{\prime }+2 x = 3 t \,{\mathrm e}^{t}
\]
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| \[
{} x^{\prime \prime }-4 x^{\prime }+3 x = 2 \,{\mathrm e}^{t}-5 \,{\mathrm e}^{2 t}
\]
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| \[
{} x^{\prime \prime }+2 x = \cos \left (\sqrt {2}\, t \right )
\]
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{} x^{\prime \prime }+4 x = \sin \left (2 t \right )
\]
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{} x^{\prime \prime }+x = 2 \sin \left (t \right )+2 \cos \left (t \right )
\]
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| \[
{} x^{\prime \prime }+9 x = \sin \left (t \right )+\sin \left (3 t \right )
\]
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