| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime \prime }+x y^{\prime }+n y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime }-x y^{\prime }-n y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime \prime }+a \left (b x -1\right ) y^{\prime \prime }+a b y^{\prime }+\lambda y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime \prime \prime }+\left (x^{2} a +b \lambda +c \right ) y^{\prime \prime }+\left (x^{2} a +\beta \lambda +\gamma \right ) y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} a^{4} x^{4} y+4 a^{3} x^{3} y^{\prime }+6 a^{2} x^{2} y^{\prime \prime }+4 a x y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime \prime } x -\left (6 x^{2}+1\right ) y^{\prime \prime \prime }+12 x^{3} y^{\prime \prime }-\left (9 x^{2}-7\right ) x^{2} y^{\prime }+2 \left (x^{2}-3\right ) x^{3} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime \prime \prime }-2 \left (\nu ^{2} x^{2}+6\right ) y^{\prime \prime }+\nu ^{2} \left (\nu ^{2} x^{2}+4\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime \prime \prime }+2 x y^{\prime \prime \prime }+a y-b \,x^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime }-\lambda ^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime \prime \prime }+\left (2 n -2 \nu +4\right ) x y^{\prime \prime \prime }+\left (n -\nu +1\right ) \left (n -\nu +2\right ) y^{\prime \prime }-\frac {b^{4} y}{16} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime \prime \prime }+2 x^{2} y^{\prime \prime \prime }-x y^{\prime \prime }+y^{\prime }-a^{4} x^{3} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime \prime \prime }-2 n \left (n +1\right ) x^{2} y^{\prime \prime }+4 n \left (n +1\right ) x y^{\prime }+\left (a \,x^{4}+n \left (n +1\right ) \left (3+n \right ) \left (n -2\right )\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }+\left (4 n^{2}-1\right ) x y^{\prime }-4 x^{4} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }-\left (4 n^{2}-1\right ) x y^{\prime }+\left (-4 x^{4}+4 n^{2}-1\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}+3\right ) x^{2} y^{\prime \prime }+\left (12 n^{2}-3\right ) x y^{\prime }-\left (4 x^{4}+12 n^{2}-3\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-\rho ^{2}-\sigma ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-\rho ^{2}-\sigma ^{2}+1\right ) x \right ) y^{\prime }+\left (\rho ^{2} \sigma ^{2}+8 x^{2}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-2 \mu ^{2}-2 \nu ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-2 \mu ^{2}-2 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (8 x^{2}+\left (\mu ^{2}-\nu ^{2}\right )^{2}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 b^{2} c^{2} x^{2 c}+6 \left (a -1\right )^{2}-2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )+1\right ) x^{2} y^{\prime \prime }+\left (4 \left (3 c -2 a +1\right ) b^{2} c^{2} x^{2 c}+\left (2 a -1\right ) \left (2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )-2 \left (a -1\right ) a -1\right )\right ) x y^{\prime }+\left (4 \left (a -c \right ) \left (a -2 c \right ) b^{2} c^{2} x^{2 c}+\left (c \mu +c \nu +a \right ) \left (c \mu +c \nu -a \right ) \left (c \mu -c \nu +a \right ) \left (c \mu -c \nu -a \right )\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a -4 c \right ) x^{3} y^{\prime \prime \prime }+\left (-2 \nu ^{2} c^{2}+2 a^{2}+4 \left (a +c -1\right )^{2}+4 \left (a -1\right ) \left (c -1\right )-1\right ) x^{2} y^{\prime \prime }+\left (2 \nu ^{2} c^{2}-2 a^{2}-\left (2 a -1\right ) \left (2 c -1\right )\right ) \left (2 a +2 c -1\right ) x y^{\prime }+\left (\left (-\nu ^{2} c^{2}+a^{2}\right ) \left (-\nu ^{2} c^{2}+a^{2}+4 a c +4 c^{2}\right )-b^{4} c^{4} x^{4 c}\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \nu ^{4} x^{4} y^{\prime \prime \prime \prime }+\left (4 \nu -2\right ) \nu ^{3} x^{3} y^{\prime \prime \prime }+\left (\nu -1\right ) \left (2 \nu -1\right ) \nu ^{2} x^{2} y^{\prime \prime }-\frac {b^{4} x^{\frac {2}{\nu }} y}{16} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+y \,{\mathrm e}^{x}-\frac {1}{x^{5}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime \prime } \sin \left (x \right )^{4}+2 y^{\prime \prime \prime } \sin \left (x \right )^{3} \cos \left (x \right )+y^{\prime \prime } \sin \left (x \right )^{2} \left (\sin \left (x \right )^{2}-3\right )+y^{\prime } \sin \left (x \right ) \cos \left (x \right ) \left (2 \sin \left (x \right )^{2}+3\right )+\left (a^{4} \sin \left (x \right )^{4}-3\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime \prime } \sin \left (x \right )^{6}+4 y^{\prime \prime \prime } \sin \left (x \right )^{5} \cos \left (x \right )-6 y^{\prime \prime } \sin \left (x \right )^{6}-4 y^{\prime } \sin \left (x \right )^{5} \cos \left (x \right )+y \sin \left (x \right )^{6}-f = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y-\lambda \left (a x -b \right ) \left (-a^{2} y+y^{\prime \prime }\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\left (5\right )}-a x y-b = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (a y^{\prime }+b y^{\prime \prime }+c y^{\prime \prime \prime }+e y^{\prime \prime \prime \prime }\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\left (5\right )}-\left (a A_{1} -A_{0} \right ) x -A_{1} -\left (\left (a A_{2} -A_{1} \right ) x +A_{2} \right ) y^{\prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime \prime \prime }-a y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{10} y^{\left (5\right )}-a y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{{5}/{2}} y^{\left (5\right )}-a y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }-6 y^{2}-x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }-6 y^{2}+4 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{2}+b x +c = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }-2 y^{3}-x y+a = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }-2 y^{3} a^{2}+2 a b x y-b = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+d +b x y+c y+a y^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a \,x^{r} y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+6 a^{10} y^{11}-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} a \sin \left (y\right )+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = \frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (n +2\right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} -y^{3}+y y^{\prime }+y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+y y^{\prime }-y^{3}+a y = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (3 a +y\right ) y^{\prime }-y^{3}+a y^{2}+2 a^{2} y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+f \left (x \right ) y^{2}+y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+f \left (x \right ) y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-3 y y^{\prime }-3 a y^{2}-4 a^{2} y-b = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+f \left (x \right ) y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 a y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y y^{\prime }+b y^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b y+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} c y+b y^{\prime }+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} b y+a y {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-a \left (x y^{\prime }-y\right )^{v} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = a \sqrt {b y^{2}+{y^{\prime }}^{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = 2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }-x y^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} b \,{\mathrm e}^{y} x +a y^{\prime }+x y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime \prime }+\left (y-1\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }-x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime } = a \left (y^{n}-y\right )
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b \,x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} b x +a y {y^{\prime }}^{2}+x^{2} y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{2} y^{\prime \prime }-\sqrt {b y^{2}+a \,x^{2} {y^{\prime }}^{2}} = 0
\]
|
✗ |
✓ |
✗ |
|