| # | ODE | Mathematica | Maple | Sympy |
| \[
{} 4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (-16 x^{2}+3\right ) y = 0
\]
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| \[
{} \left (2 x +1\right ) x y^{\prime \prime }-2 \left (2 x^{2}-1\right ) y^{\prime }-4 \left (1+x \right ) y = 0
\]
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| \[
{} \left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }+\left (-2+2 x \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (1+4 x \right ) y^{\prime }+\left (4 x +2\right ) y = 0
\]
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| \[
{} \left (3 x -1\right ) y^{\prime \prime }-\left (2+3 x \right ) y^{\prime }-\left (6 x -8\right ) y = 0
\]
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| \[
{} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\]
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| \[
{} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0
\]
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| \[
{} y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0
\]
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| \[
{} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-5 t y^{\prime }+9 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\]
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| \[
{} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\]
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| \[
{} \left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\]
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| \[
{} \left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-t y^{\prime }+2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0
\]
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| \[
{} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\]
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| \[
{} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+\alpha t y^{\prime }+\beta y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+5 t y^{\prime }-2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+2 t y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime \prime }-\frac {2 \left (t +1\right ) y^{\prime }}{t^{2}+2 t -1}+\frac {2 y}{t^{2}+2 t -1} = 0
\]
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| \[
{} y^{\prime \prime }-4 t y^{\prime }+\left (4 t^{2}-2\right ) y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} \left (t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\]
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| \[
{} \left (-t^{2}+1\right ) y^{\prime \prime }-2 t y^{\prime }+6 y = 0
\]
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| \[
{} \left (2 t +1\right ) y^{\prime \prime }-4 \left (t +1\right ) y^{\prime }+4 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0
\]
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| \[
{} t y^{\prime \prime }-\left (1+3 t \right ) y^{\prime }+3 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+5 t y^{\prime }-5 y = 0
\]
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| \[
{} 2 t^{2} y^{\prime \prime }+3 t y^{\prime }-y = 0
\]
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| \[
{} \left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\]
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| \[
{} \left (t -2\right )^{2} y^{\prime \prime }+5 \left (t -2\right ) y^{\prime }+4 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t y^{\prime }+y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+3 t y^{\prime }+2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-t y^{\prime }-2 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0
\]
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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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| \[
{} \left (1-x \right ) y^{\prime \prime } = y^{\prime }
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+2 \left (1+y^{\prime }\right ) x = 0
\]
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| \[
{} \left (-{\mathrm e}^{x}+1\right ) y^{\prime \prime } = {\mathrm e}^{x} y^{\prime }
\]
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| \[
{} \left (x -2\right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}} = 0
\]
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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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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }-8 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y = 0
\]
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| \[
{} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+5 y = 0
\]
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| \[
{} t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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| \[
{} y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y = 0
\]
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| \[
{} 4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
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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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