| # | ODE | Mathematica | Maple | Sympy |
| \[
{} a \left (x^{2}-1\right )^{2} y^{\prime \prime }+b x \left (x^{2}-1\right ) y^{\prime }+\left (c \,x^{2}+d x +e \right ) y = 0
\]
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| \[
{} \left (x^{2} a +b \right )^{2} y^{\prime \prime }+\left (2 a x +c \right ) \left (x^{2} a +b \right ) y^{\prime }+k y = 0
\]
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| \[
{} \left (x^{2} a +b \right )^{2} y^{\prime \prime }+\left (x^{2} a +b \right ) \left (c \,x^{2}+d \right ) y^{\prime }+2 \left (-a d +b c \right ) x y = 0
\]
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| \[
{} \left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-\left (b \,x^{n +1}+a \right ) y = 0
\]
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| \[
{} \left (x^{2}+a \right )^{2} y^{\prime \prime }+b \,x^{n} \left (x^{2}+a \right ) y^{\prime }-m \left (b \,x^{n +1}+\left (m -1\right ) x^{2}+a \right ) y = 0
\]
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✗ |
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| \[
{} \left (x -a \right )^{2} \left (x -b \right )^{2} y^{\prime \prime }-c y = 0
\]
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| \[
{} \left (x -a \right )^{2} \left (x -b \right )^{2} y^{\prime \prime }+\left (x -a \right ) \left (x -b \right ) \left (2 x +\lambda \right ) y^{\prime }+\mu y = 0
\]
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✓ |
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| \[
{} \left (x^{2} a +b x +c \right )^{2} y^{\prime \prime }+A y = 0
\]
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✓ |
✓ |
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| \[
{} \left (x^{2}-1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}-1\right ) y^{\prime }+\left (\left (x^{2}-1\right ) \left (a^{2} x^{2}-\lambda \right )-m^{2}\right ) y = 0
\]
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✓ |
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| \[
{} \left (x^{2}+1\right )^{2} y^{\prime \prime }+2 x \left (x^{2}+1\right ) y^{\prime }+\left (\left (x^{2}+1\right ) \left (a^{2} x^{2}-\lambda \right )+m^{2}\right ) y = 0
\]
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✓ |
✗ |
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| \[
{} \left (x^{2} a +b x +c \right )^{2} y^{\prime \prime }+\left (2 a x +k \right ) \left (x^{2} a +b x +c \right ) y^{\prime }+m y = 0
\]
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✓ |
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| \[
{} a y-x^{5} y^{\prime }+x^{6} y^{\prime \prime } = 0
\]
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✓ |
✓ |
✓ |
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| \[
{} x^{6} y^{\prime \prime }+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+b y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} x^{n} y^{\prime \prime }+c \left (a x +b \right )^{n -4} y = 0
\]
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✗ |
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✗ |
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| \[
{} x^{n} y^{\prime \prime }+a x y^{\prime }-\left (b^{2} x^{n}+2 b \,x^{n -1}+a b x +a \right ) y = 0
\]
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✗ |
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| \[
{} x^{n} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\]
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✗ |
✓ |
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| \[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n -1}+b x \right ) y^{\prime }+\left (a -1\right ) y = 0
\]
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✗ |
✓ |
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| \[
{} x^{n} y^{\prime \prime }+\left (2 x^{n -1}+x^{2} a +b x \right ) y^{\prime }+b y = 0
\]
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✗ |
✓ |
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| \[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }+c \left (\left (a -c \right ) x^{n}+b \right ) y = 0
\]
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| \[
{} x^{n} y^{\prime \prime }+\left (a \,x^{n}-x^{n -1}+a b x +b \right ) y^{\prime }+y a^{2} b x = 0
\]
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| \[
{} x^{n} y^{\prime \prime }+\left (a \,x^{m +n}+1\right ) y^{\prime }+a \,x^{m} \left (1+m \,x^{n -1}\right ) y = 0
\]
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| \[
{} \left (a \,x^{n}+b \right ) y^{\prime \prime }+\left (c \,x^{n}+d \right ) y^{\prime }+\lambda \left (\left (-a \lambda +c \right ) x^{n}+d -b \lambda \right ) y = 0
\]
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| \[
{} \left (a \,x^{n}+b x +c \right ) y^{\prime \prime } = a n \left (n -1\right ) x^{n -2} y
\]
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✗ |
✓ |
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| \[
{} x \left (x^{n}+1\right ) y^{\prime \prime }+\left (\left (a -b \right ) x^{n}+a -n \right ) y^{\prime }+b \left (1-a \right ) x^{n -1} y = 0
\]
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✓ |
✓ |
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| \[
{} x \left (x^{2 n}+a \right ) y^{\prime \prime }+\left (x^{2 n}+a -a n \right ) y^{\prime }-b^{2} x^{-1+2 n} y = 0
\]
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✓ |
✓ |
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| \[
{} x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a^{2} \left (n +1\right ) x^{2 n}+n -1\right ) y^{\prime }-\nu \left (\nu +1\right ) a^{2} n^{2} x^{2 n} y = 0
\]
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✓ |
✓ |
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| \[
{} x^{2} \left (a^{2} x^{2 n}-1\right ) y^{\prime \prime }+x \left (a p \,x^{n}+q \right ) y^{\prime }+\left (a r \,x^{n}+s \right ) y = 0
\]
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✓ |
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| \[
{} \left (x^{n}+a \right )^{2} y^{\prime \prime }-b \,x^{n -2} \left (\left (b -1\right ) x^{n}+a \left (n -1\right )\right ) y = 0
\]
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✗ |
✓ |
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| \[
{} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) \left (c \,x^{n}+d \right ) y^{\prime }+n \left (-a d +b c \right ) x^{n -1} y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} \left (x^{n}+a \right )^{2} y^{\prime \prime }+b \,x^{m} \left (x^{n}+a \right ) y^{\prime }-x^{n -2} \left (b \,x^{1+m}+a n -a \right ) y = 0
\]
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✗ |
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| \[
{} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+c \,x^{m} \left (a \,x^{n}+b \right ) y^{\prime }+\left (c \,x^{m}-a n \,x^{n -1}-1\right ) y = 0
\]
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✗ |
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| \[
{} x^{2} \left (a \,x^{n}+b \right )^{2} y^{\prime \prime }+\left (n +1\right ) x \left (a^{2} x^{2 n}-b^{2}\right ) y^{\prime }+c y = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} \left (a \,x^{n +1}+b \,x^{n}+c \right )^{2} y^{\prime \prime }+\left (\alpha \,x^{n}+\beta \,x^{n -1}+\gamma \right ) y^{\prime }+\left (n \left (-a n -a +\alpha \right ) x^{n -1}+\left (n -1\right ) \left (-n b +\beta \right ) x^{n -2}\right ) y = 0
\]
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✗ |
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| \[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda -x \right ) y^{\prime }+y = 0
\]
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✗ |
✓ |
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| \[
{} \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+\left (\lambda ^{2}-x^{2}\right ) y^{\prime }+\left (x +\lambda \right ) y = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} 2 \left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime \prime }+a n \,x^{n -1} b m \,x^{m -1} y^{\prime }+y d = 0
\]
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| \[
{} \left (a \,x^{n}+b \right )^{1+m} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime }-a n m \,x^{n -1} y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{x}-b \right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+a \left (\lambda \,{\mathrm e}^{\lambda x}-a \,{\mathrm e}^{2 \lambda x}\right ) y = 0
\]
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✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\left (a^{2} {\mathrm e}^{2 x}+a \left (2 b +1\right ) {\mathrm e}^{x}+b^{2}\right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }-\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+c \right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{4 \lambda x}+b \,{\mathrm e}^{3 \lambda x}+c \,{\mathrm e}^{2 \lambda x}-\frac {\lambda ^{2}}{4}\right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}-\frac {\lambda ^{2}}{4}\right ) y = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime } = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 a x} y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+a y^{\prime }+\left (b \,{\mathrm e}^{\lambda x}+c \right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{3 \lambda x}+b \,{\mathrm e}^{2 \lambda x}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }-y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x} \left (b \,{\mathrm e}^{\lambda x}+c \right )^{n}+\frac {1}{4}-\frac {\lambda ^{2}}{4}\right ) y = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+2 a \,{\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left ({\mathrm e}^{\lambda x} a +\lambda \right ) y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (a +b \right ) {\mathrm e}^{\lambda x} y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{\lambda x}+\lambda \right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{x \mu } \left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+\mu \right ) y = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+2 k \,{\mathrm e}^{x \mu } y^{\prime }+\left (a \,{\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{\lambda x}+k^{2} {\mathrm e}^{2 x \mu }+k \mu \,{\mathrm e}^{x \mu }+c \right ) y = 0
\]
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✓ |
✗ |
✗ |
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| \[
{} y^{\prime \prime }-\left (a +2 b \,{\mathrm e}^{a x}\right ) y^{\prime }+b^{2} {\mathrm e}^{2 a x} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{2 \lambda x}+\lambda \right ) y^{\prime }-a \lambda \,{\mathrm e}^{2 \lambda x} y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+b \,{\mathrm e}^{2 \lambda x} y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime }+c \left ({\mathrm e}^{\lambda x} a +b -c \right ) y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (a +b \,{\mathrm e}^{2 \lambda x}\right ) y^{\prime }+\lambda \left (a -\lambda -b \,{\mathrm e}^{2 \lambda x}\right ) y = 0
\]
|
✓ |
✗ |
✗ |
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| \[
{} y^{\prime \prime }+\left (a +b \,{\mathrm e}^{\lambda x}+b -3 \lambda \right ) y^{\prime }+a^{2} \lambda \left (b -\lambda \right ) {\mathrm e}^{2 \lambda x} y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+c \,{\mathrm e}^{x \mu }\right ) y = 0
\]
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✓ |
✗ |
✗ |
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| \[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a +b \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a \left (b +\lambda \right ) {\mathrm e}^{\lambda x}+c \right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +2 b -\lambda \right ) y^{\prime }+\left (c \,{\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+b^{2}-b \lambda \right ) y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{x}+b \right ) y^{\prime }+\left (c \left (a -c \right ) {\mathrm e}^{2 x}+\left (a k +b c -2 c k +c \right ) {\mathrm e}^{x}+k \left (b -k \right )\right ) y = 0
\]
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✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime }+\left (\alpha \,{\mathrm e}^{2 \lambda x}+\beta \,{\mathrm e}^{\lambda x}+\gamma \right ) y = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+b \,{\mathrm e}^{2 x \mu }+c \,{\mathrm e}^{x \mu }+k \right ) y = 0
\]
|
✓ |
✗ |
✗ |
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| \[
{} y^{\prime \prime }+\left (2 \,{\mathrm e}^{\lambda x} a +b -\lambda \right ) y^{\prime }+\left (a^{2} {\mathrm e}^{2 \lambda x}+a b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 x \mu }+d \,{\mathrm e}^{x \mu }+k \right ) y = 0
\]
|
✓ |
✗ |
✗ |
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| \[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }\right ) y^{\prime }+a \,{\mathrm e}^{\lambda x} \left (b \,{\mathrm e}^{x \mu }+\lambda \right ) y = 0
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime \prime }+{\mathrm e}^{\lambda x} \left (a \,{\mathrm e}^{2 x \mu }+b \right ) y^{\prime }+\mu \left ({\mathrm e}^{\lambda x} \left (b -a \,{\mathrm e}^{2 x \mu }\right )-\mu \right ) y = 0
\]
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✗ |
✓ |
✗ |
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| \[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+c \right ) y^{\prime }+\left (a \lambda \,{\mathrm e}^{\lambda x}+b \mu \,{\mathrm e}^{x \mu }\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{x \mu }+c \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+{\mathrm e}^{\lambda x} a c +b \mu \,{\mathrm e}^{x \mu }\right ) y = 0
\]
|
✗ |
✗ |
✗ |
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| \[
{} y^{\prime \prime }+\left ({\mathrm e}^{\lambda x} a +2 b \,{\mathrm e}^{x \mu }-\lambda \right ) y^{\prime }+\left (a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+c \,{\mathrm e}^{2 \lambda x}+b^{2} {\mathrm e}^{2 x \mu }+b \left (\mu -\lambda \right ) {\mathrm e}^{x \mu }\right ) y = 0
\]
|
✓ |
✗ |
✗ |
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| \[
{} y^{\prime \prime }+\left (a \,{\mathrm e}^{\left (\lambda +\mu \right ) x}+a \lambda \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{x \mu }-2 \lambda \right ) y^{\prime }+a^{2} b \lambda \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x} y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+a \,{\mathrm e}^{b \,x^{n}} y^{\prime }+c \left (a \,{\mathrm e}^{b \,x^{n}}-c \right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }-a \,\lambda ^{2} {\mathrm e}^{\lambda x} y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (a^{2} {\mathrm e}^{2 \lambda x}+b \right ) y^{\prime \prime }-b \lambda y^{\prime }-a^{2} \lambda ^{2} k^{2} {\mathrm e}^{2 \lambda x} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }+a \lambda \,{\mathrm e}^{\lambda x} y^{\prime }+c y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+k \left (\left (-a k +c \right ) {\mathrm e}^{\lambda x}+d -b k \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left ({\mathrm e}^{\lambda x} a +b \right ) y^{\prime \prime }+\left (c \,{\mathrm e}^{\lambda x}+d \right ) y^{\prime }+\left (n \,{\mathrm e}^{\lambda x}+m \right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \frac {2 x y+1}{y}+\frac {\left (y-x \right ) y^{\prime }}{y^{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \frac {y^{2}-2 x^{2}}{x y^{2}-x^{3}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y} = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \frac {1}{\sqrt {x^{2}+y^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {x^{2}+y^{2}}}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x y^{\prime }+x +y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sec \left (x \right ) \cos \left (y\right )^{2}-\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (1+x \right ) y^{2}-x^{3} y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right ) = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
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| \[
{} {\mathrm e}^{\frac {y}{x}} x +y-x y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2} y+3 y^{3}-\left (x^{3}+2 x y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{2} y^{\prime }+y^{2}-x y = 0
\]
|
✓ |
✓ |
✓ |
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| \[
{} 2 x^{2} y+y^{3}-x^{3} y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{3}+x^{3} y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x +y \cos \left (\frac {y}{x}\right )-x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left (x +y+1\right ) y^{\prime }+1+4 x +3 y = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 4 x -y+2+\left (x +y+3\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 x +y-\left (4 x +2 y-1\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} 2 y+3 x y^{2}+\left (x +2 x^{2} y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0
\]
|
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| \[
{} y^{\prime }+y \cot \left (x \right ) = \sec \left (x \right )
\]
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