| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+b x y^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} a y y^{\prime }+2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a y y^{\prime }-2 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 y y^{\prime }-4 x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y y^{\prime \prime }+\left (\frac {a x}{\sqrt {b^{2}-x^{2}}}-x \right ) {y^{\prime }}^{2}-y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (x +y\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (y-1\right ) y^{\prime \prime }-2 x^{2} {y^{\prime }}^{2}-2 x \left (y-1\right ) y^{\prime }-2 y \left (y-1\right )^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} x^{2} \left (x +y\right ) y^{\prime \prime }-\left (x y^{\prime }-y\right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (x -y\right ) y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2} y y^{\prime \prime }-x^{2} \left (1+{y^{\prime }}^{2}\right )+y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a \,x^{2} y y^{\prime \prime }+b \,x^{2} {y^{\prime }}^{2}+c x y y^{\prime }+d y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (1+x \right )^{2} y y^{\prime \prime }-x \left (1+x \right )^{2} {y^{\prime }}^{2}+2 \left (1+x \right )^{2} y y^{\prime }-a \left (x +2\right ) y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1-2 y\right ) {y^{\prime }}^{2}+\left (1+y^{2}\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (x y^{\prime }-y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime }-2 \left (1+{y^{\prime }}^{2}\right ) \left (x y^{\prime }-y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1-y\right ) y y^{\prime \prime }-\left (1-2 y\right ) {y^{\prime }}^{2}+f \left (x \right ) \left (1-y\right ) y y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (1-y\right ) y y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 3 \left (1-y\right ) y y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a y \left (y-1\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a y \left (y-1\right ) y^{\prime \prime }-\left (a -1\right ) \left (2 y-1\right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a b y \left (y-1\right ) y^{\prime \prime }-\left (\left (2 a b -a -b \right ) y+\left (1-a \right ) b \right ) {y^{\prime }}^{2}+f y \left (y-1\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2} y \left (y-1\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (y-1\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (y-1\right )^{3}+c x y^{2} \left (y-1\right )+d \,x^{2} y^{2} \left (1+y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x +y\right ) \left (x y^{\prime }-y\right )^{3}+x^{3} y^{2} y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1-3 y^{2}\right ) {y^{\prime }}^{2}+y \left (1+y^{2}\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (y^{2}-1\right ) \left (a^{2} y^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-a^{2} y^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 a^{2} y^{2}\right ) y {y^{\prime }}^{2} = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} \left (c +2 b x +x^{2} a +y^{2}\right )^{2} y^{\prime \prime }+y d = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} h \left (y\right ) y^{\prime \prime }+a h \left (y\right ) {y^{\prime }}^{2}+j \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} \left (x y^{\prime }-y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x y^{\prime }-y\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y+3 x y^{\prime }+2 {y^{\prime }}^{3} y+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{3}+\left ({y^{\prime }}^{2}+y^{2}\right ) y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} 2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 4 {y^{\prime }}^{2}-2 \left (3 x y^{\prime }+y\right ) y^{\prime \prime }+3 x^{2} {y^{\prime \prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (2-9 x \right ) x^{2} {y^{\prime \prime }}^{2}-6 \left (1-6 x \right ) x y^{\prime } y^{\prime \prime }+6 y y^{\prime \prime }-36 x {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a^{2} y^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (x y^{\prime }-y\right )^{3} = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} 32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3}+\left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )^{3} = 0
\]
|
✓ |
✗ |
✗ |
|
| \[
{} \sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }-f \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime \prime } = {\mathrm e}^{y}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2} = 0
\]
|
✗ |
✓ |
✓ |
|
| \[
{} \left (x y^{\prime }-y\right )^{2}+x^{2} y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{3} y^{\prime \prime }-\left (x y^{\prime }-y\right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = \ln \left (y\right ) y^{2}-x^{2} y^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime }+y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+\left (5 x^{4}-6 x^{2}\right ) x^{\prime }+x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+\left (1+x^{2}\right ) x^{\prime }+x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+\frac {2 {y^{\prime }}^{2}}{1-y} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = 3 \sqrt {y}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = \frac {y y^{\prime }}{\sqrt {x^{2}+1}}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}+{y^{\prime \prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} m x^{\prime \prime } = f \left (x\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} m x^{\prime \prime } = f \left (x^{\prime }\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -y y^{\prime }-x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime } = y^{\prime } \ln \left (\frac {y^{\prime }}{x}\right )
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = 2 y^{3}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sinh \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = x y
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime \prime }+\frac {k x}{y^{4}} = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime \prime }-x {y^{\prime }}^{2} \sin \left (y\right )+2 \left (\cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime } = \sin \left (x \right ) y
\]
|
✗ |
✓ |
✗ |
|
| \[
{} \left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y^{\prime \prime } = \frac {a}{y^{3}}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} -{y^{\prime }}^{2}+{y^{\prime }}^{3}+y y^{\prime \prime } = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = \frac {1}{2 y^{\prime }}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} x^{\prime \prime }+x-x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+x+x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{\prime \prime }+x^{\prime }+x-x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime }+x^{\prime }+x+x^{3} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right )
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime \prime } = 4 x \sqrt {y^{\prime }}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y y^{\prime \prime } = -{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime \prime } = -y^{\prime }+{y^{\prime }}^{2}
\]
|
✓ |
✓ |
✓ |
|
| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = y^{\prime }
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (y-3\right ) y^{\prime \prime } = 2 {y^{\prime }}^{2}
\]
|
✓ |
✓ |
✗ |
|