| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0
\]
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| \[
{} -a^{2} x^{3} y-y^{\prime }+x y^{\prime \prime } = 0
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| \[
{} \left ({\mathrm e}^{x^{2}}-k^{2}\right ) x^{3} y-y^{\prime }+x y^{\prime \prime } = 0
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| \[
{} 2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} 2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -x y+2 y^{\prime }+x y^{\prime \prime } = {\mathrm e}^{x}
\]
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| \[
{} a x y+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} a \,x^{2} y+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} y+\left (1-a \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -y+2 n y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} b y+a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} b x y+a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} b \,x^{k} y+a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} y-y^{\prime } \left (1+x \right )+x y^{\prime \prime } = 0
\]
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| \[
{} n y+\left (1-x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} n y+\left (1+k -x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} 2 \left (1-x \right ) y-y^{\prime } \left (1+x \right )+x y^{\prime \prime } = 0
\]
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| \[
{} -y-\left (2-x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} 3 y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime } = 0
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| \[
{} b y+\left (x +a \right ) y^{\prime }+x y^{\prime \prime } = 0
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| \[
{} -a y+\left (c -x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -\left (1-x \right ) y+\left (1-2 x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = x^{2}-x -1
\]
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| \[
{} c y+\left (b x +a \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} \left (b x +2 a \right ) y-2 \left (b x +a \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} \left (a b x +a n +b m \right ) y+\left (m +n +x \left (a +b \right )\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -y^{\prime } \left (-x^{2}+1\right )+x y^{\prime \prime } = 0
\]
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| \[
{} 2 x y-\left (-x^{2}+4\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 4 x^{3} {\mathrm e}^{-x^{2}}
\]
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| \[
{} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} a \,x^{2} \left (a \,x^{3}+1\right ) y-\left (-2 a \,x^{3}+1\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} f \left (x \right ) y+\left (2+f \left (x \right ) x \right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = 0
\]
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| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = \left (1-x \right )^{2}
\]
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| \[
{} 3 \left (2-x \right ) y-\left (9-4 x \right ) y^{\prime }+\left (3-x \right ) y^{\prime \prime } = 0
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| \[
{} -2 y^{\prime }+\left (a -x \right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (x +a \right ) y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime }+2 x y^{\prime \prime } = 0
\]
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| \[
{} a y+y^{\prime }+2 x y^{\prime \prime } = 0
\]
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| \[
{} -a y+y^{\prime }+2 x y^{\prime \prime } = 0
\]
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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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