| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = \frac {5 \ln \left (x \right )}{x^{2}}
\]
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| \[
{} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+3 y = 60 \cos \left (3 t \right )
\]
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| \[
{} y^{\prime \prime }+y^{\prime }-2 y = 9 \,{\mathrm e}^{-2 t}
\]
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 2 t^{2}+1
\]
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{} y^{\prime \prime }+4 y = 8 \sin \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t}
\]
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{} y^{\prime \prime }-2 y^{\prime }+2 y = 8 \sin \left (t \right ) {\mathrm e}^{-t}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t} \sin \left (2 t \right )
\]
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| \[
{} y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t}
\]
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| \[
{} y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right )
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right )
\]
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{} y^{\prime \prime }+4 y = 8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )
\]
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{} y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right )
\]
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{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right )
\]
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| \[
{} y^{\prime \prime }-5 y^{\prime }+6 y = \delta \left (t -2\right )
\]
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{} y^{\prime \prime }+4 y = 4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right )
\]
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| \[
{} y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = x +\sin \left (x \right )
\]
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| \[
{} y^{\prime \prime } = \operatorname {c1} \cos \left (a x \right )+\operatorname {c2} \sin \left (b x \right )
\]
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| \[
{} y^{\prime \prime } = x \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime } = \operatorname {c1} \,{\mathrm e}^{a x}+\operatorname {c2} \,{\mathrm e}^{-b x}
\]
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| \[
{} y^{\prime \prime }+y = 0
\]
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| \[
{} y^{\prime \prime }-y = 0
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| \[
{} y^{\prime \prime }+y = a x
\]
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| \[
{} y^{\prime \prime }+y = a \cos \left (b x \right )
\]
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{} y^{\prime \prime }+y = 8 \cos \left (x \right ) \cos \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }+y = \sec \left (x \right )
\]
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| \[
{} y^{\prime \prime }+y = a \sin \left (b x \right )
\]
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| \[
{} y^{\prime \prime }+y = \sin \left (a x \right ) \sin \left (b x \right )
\]
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| \[
{} y^{\prime \prime }+y = 4 x \sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }+y = x \left (\cos \left (x \right )-x \sin \left (x \right )\right )
\]
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| \[
{} y^{\prime \prime }+y = \tan \left (x \right )^{2}
\]
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| \[
{} y^{\prime \prime }+y = {\mathrm e}^{-x}
\]
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| \[
{} y^{\prime \prime }+y = {\mathrm e}^{x} \left (x^{2}-1\right )
\]
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| \[
{} y^{\prime \prime }+y = \sin \left (2 x \right ) {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }+y = {\mathrm e}^{2 x} \cos \left (x \right )
\]
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| \[
{} y^{\prime \prime }-2 y = 0
\]
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| \[
{} y^{\prime \prime }-2 y = 4 x^{2} {\mathrm e}^{x^{2}}
\]
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| \[
{} y^{\prime \prime }+4 y = 0
\]
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| \[
{} y^{\prime \prime }+4 y = x \sin \left (x \right )^{2}
\]
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| \[
{} y^{\prime \prime }+4 y = 2 \tan \left (x \right )
\]
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{} y^{\prime \prime }+4 y = 2 \tan \left (x \right )
\]
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| \[
{} -a^{2} y+y^{\prime \prime } = 1+x
\]
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| \[
{} y^{\prime \prime } = a x +b y
\]
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| \[
{} y^{\prime \prime }+a^{2} y = x^{2}+x +1
\]
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| \[
{} y^{\prime \prime }+a^{2} y = \cos \left (b x \right )
\]
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| \[
{} y^{\prime \prime }+a^{2} y = \cot \left (a x \right )
\]
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| \[
{} y^{\prime \prime }+a^{2} y = \sin \left (b x \right )
\]
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| \[
{} y^{\prime \prime }+x y = 0
\]
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| \[
{} \left (b x +a \right ) y+y^{\prime \prime } = 0
\]
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| \[
{} \left (x^{2}+a \right ) y+y^{\prime \prime } = 0
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| \[
{} \left (-x^{2}+a \right ) y+y^{\prime \prime } = 0
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| \[
{} y^{\prime \prime } = \left (x^{2}+a \right ) y
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| \[
{} \left (b^{2} x^{2}+a \right ) y+y^{\prime \prime } = 0
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| \[
{} \left (c \,x^{2}+b x +a \right ) y+y^{\prime \prime } = 0
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| \[
{} \left (x^{4}+\operatorname {a1} \,x^{2}+\operatorname {a0} \right ) y+y^{\prime \prime } = 0
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| \[
{} a \,x^{k} y+y^{\prime \prime } = 0
\]
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| \[
{} \left (a +b \cos \left (2 x \right )\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} \left (a +b \cos \left (2 x \right )+k \cos \left (4 x \right )\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = 2 \csc \left (x \right )^{2} y
\]
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| \[
{} a \csc \left (x \right )^{2} y+y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}+\operatorname {a2} \csc \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = \left (a^{2}+\left (-1+p \right ) p \csc \left (x \right )^{2}+\left (-1+q \right ) q \sec \left (x \right )^{2}\right ) y
\]
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{} \left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
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{} y^{\prime \prime } = \left (1+2 \tan \left (x \right )^{2}\right ) y
\]
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| \[
{} -\left (a^{2}-b \,{\mathrm e}^{x}\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} -\left (a^{2}-{\mathrm e}^{2 x}\right ) y+y^{\prime \prime } = 0
\]
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{} \left (a +b \,{\mathrm e}^{x}+c \,{\mathrm e}^{2 x}\right ) y+y^{\prime \prime } = 0
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| \[
{} a \,{\mathrm e}^{b x} y+y^{\prime \prime } = 0
\]
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| \[
{} \left (a +b \cosh \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
\]
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| \[
{} \left (a +b \sinh \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
\]
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{} \left (a +b \sin \left (x \right )^{2}\right ) y+y^{\prime \prime } = 0
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| \[
{} \frac {\left (a +b \right ) y}{x^{2}}+y^{\prime \prime } = 0
\]
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| \[
{} x y-y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+y = 0
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = \left (x -6\right ) x^{2}
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \left (3 x^{2}+2 x +1\right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \sin \left (x \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{2 x}+x^{2}-\cos \left (x \right )
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = 8 x^{2} {\mathrm e}^{3 x}
\]
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{} y^{\prime \prime }-2 y^{\prime }+y = 50 \cosh \left (x \right ) \cos \left (x \right )
\]
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| \[
{} 3 y+2 y^{\prime }+y^{\prime \prime } = 0
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{} y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \cos \left (x \right )
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 0
\]
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{} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \sinh \left (x \right )
\]
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{} \csc \left (a \right )^{2} y-2 \tan \left (a \right ) y^{\prime }+y^{\prime \prime } = 0
\]
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{} \csc \left (a \right )^{2} y-2 \tan \left (a \right ) y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x \tan \left (a \right )} x^{2}
\]
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| \[
{} y^{\prime \prime }+3 y^{\prime }+2 y = 0
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{} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (a x \right )
\]
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{} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}+\sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = 2 \,{\mathrm e}^{-x}+x^{2}
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{a x} x
\]
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| \[
{} -4 y-3 y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} -4 y-3 y^{\prime }+y^{\prime \prime } = 10 \cos \left (2 x \right )
\]
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{} y^{\prime \prime }-4 y^{\prime }+4 y = 0
\]
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{} y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 x} \cos \left (x \right )^{2}
\]
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| \[
{} 5 y+4 y^{\prime }+y^{\prime \prime } = 0
\]
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