| # | ODE | Mathematica | Maple | Sympy |
| \[
{} -a y+y^{\prime }+2 x y^{\prime \prime } = 0
\]
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| \[
{} \left (b x +a \right ) y+y^{\prime }+2 x y^{\prime \prime } = 0
\]
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| \[
{} -x y-\left (2 x^{2}+1\right ) y^{\prime }+2 x y^{\prime \prime } = 0
\]
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| \[
{} -y-\left (x +2\right ) y^{\prime }+\left (1-2 x \right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (3-x \right ) y-\left (4-3 x \right ) y^{\prime }+\left (1-2 x \right ) y^{\prime \prime } = 0
\]
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| \[
{} y+2 y^{\prime }+4 y^{\prime \prime } = 0
\]
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| \[
{} -y-2 y^{\prime }+4 y^{\prime \prime } = 0
\]
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| \[
{} y+4 \coth \left (x \right ) y^{\prime }+4 x y^{\prime \prime } = 0
\]
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| \[
{} \left (b x +a \right ) y+8 y^{\prime }+16 x y^{\prime \prime } = 0
\]
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| \[
{} c y^{\prime }+\left (b x +a \right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime } = 0
\]
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| \[
{} y-x y^{\prime }+\left (1-x \cot \left (x \right )\right ) y^{\prime \prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime } = b x +a
\]
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| \[
{} x^{2} y^{\prime \prime } = 2 y
\]
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| \[
{} x^{2} y^{\prime \prime } = 6 y
\]
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| \[
{} x^{2} y^{\prime \prime } = 12 y
\]
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| \[
{} a y+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (b x +a \right ) y+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime } = x^{4}
\]
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| \[
{} -\left (a^{2} x^{2}+2\right ) y+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (-a^{2} x^{2}+6\right ) y+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (n \left (n +1\right )+a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (\left (n -1\right ) n -a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (\left (a -1\right ) a -b \,x^{k}\right ) y+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} x^{k} \left (a +b \,x^{k}\right ) y+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -b \left (b \,x^{2}+a \right ) y+a y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} a
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = x^{2} \left (x +3\right )
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 3 x^{3}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }-3 y = 0
\]
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| \[
{} -a^{2} y+x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (b x +a \right ) y+x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (p^{2}-x^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (p^{2}+x^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (i x^{2}+p^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (-a^{2} x^{2}+p^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (c \,x^{2}+b x +a \right ) y+x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (-x^{4}+4 x^{2} a +n^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (c^{2} x^{4}+b^{2} x^{2}+a^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (1+m \right ) x^{m} a \left (m \right ) y+x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -y+\left (x +a \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 4 x^{3}
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{3} \sin \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 2 x \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{5} \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 2-x
\]
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| \[
{} \left (a^{2} x^{2}+2\right ) y-2 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (n \left (n +1\right )-a^{2} x^{2}\right ) y+2 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (b \,x^{2}+a \right ) y+2 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} a y-2 \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = a -x +x \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 5 x
\]
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| \[
{} -5 y-3 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -5 y-3 x y^{\prime }+x^{2} y^{\prime \prime } = x^{2} \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x}
\]
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| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \ln \left (1+x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{2} \left (x^{2}-1\right )
\]
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| \[
{} \left (-x^{2}+2\right ) y+4 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (x^{2}+6\right ) y+4 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} 13 y+5 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} 16 y-7 x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (a \left (a +1\right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \operatorname {a2} y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b2} \,x^{2}+\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {c2} \,x^{2}+\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (c \,x^{3}+b \right ) y+a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} x^{2} \left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y+a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (b +c \,x^{2 k}\right ) y+a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} c y+\left (b x +a \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} a \left (a +1\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} a \left (a +1\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime } = {\mathrm e}^{x} x^{2+a}
\]
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| \[
{} \left (a \left (a +1\right )+b^{2} x^{2}\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (b x +a \right ) y+2 a x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -2 x^{2} y-x^{2} y^{\prime }+x^{2} y^{\prime \prime } = 1+x +2 x^{2} \ln \left (x \right )
\]
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| \[
{} \left (b \,x^{2}+a \right ) y+x^{2} y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -y-y^{\prime } \left (-x^{2}+1\right )+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -\left (1-x \right ) y+x \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\]
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| \[
{} -\left (2+3 x \right ) y+\left (2-x \right ) x y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -y+x \left (x +3\right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} 2 \left (1+x \right ) y-2 x \left (1+x \right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} -2 y+a \,x^{2} y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (3 a x +5\right ) y-x \left (a x +5\right ) y^{\prime }+x^{2} y^{\prime \prime } = 0
\]
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