| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
0.717 |
|
| \begin{align*}
6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.791 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
3 x^{2} y^{3}+y^{4}+\left (3 x^{3} y^{2}+y^{4}+4 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
0.599 |
|
| \begin{align*}
6 x y^{3}+2 y^{4}+\left (9 x^{2} y^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.827 |
|
| \begin{align*}
2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.235 |
|
| \begin{align*}
6 x^{2} y^{2}+4 x^{3} y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.219 |
|
| \begin{align*}
14 x^{2} y^{3}+21 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
\left (x +y\right )^{2}+\left (x +y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.180 |
|
| \begin{align*}
2 y^{3}+3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
27 x y^{2}+8 y^{3}+\left (18 x^{2} y+12 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
0.742 |
|
| \begin{align*}
a \cos \left (x \right ) y-\sin \left (x \right ) y^{2}+\left (b \cos \left (x \right ) y-x \sin \left (x \right ) y\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.806 |
|
| \begin{align*}
x^{4} y^{4}+x^{5} y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
4 y^{2}&={y^{\prime }}^{2} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+x y y^{\prime }-2 x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (x +y-2 y x \right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (y^{2}-x^{3}-x y^{2}\right ) y^{\prime }-x y \left (x^{2}+y^{2}\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
y^{2}-2 x y y^{\prime }+{y^{\prime }}^{2} \left (x^{2}-1\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
{y^{\prime }}^{2}-3 y^{\prime }+2&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.263 |
|
| \begin{align*}
y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
x +\left (2-x +2 y\right ) y^{\prime }&=x y \left (y^{\prime }-1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| \begin{align*}
\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.988 |
|
| \begin{align*}
\left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
10.968 |
|
| \begin{align*}
\left (1-x^{2} y^{2}\right ) y^{\prime }&=\left (y x +1\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.545 |
|
| \begin{align*}
x \left (-y x +1\right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (y x +1\right ) \left (1+x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
{y^{\prime }}^{2}&=y^{2} a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.414 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x^{2} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
{y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
{y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-3 x^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.533 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 x y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.493 |
|
| \begin{align*}
y y^{\prime }+{y^{\prime }}^{2}&=x \left (x +y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.279 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.929 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (1+2 y x \right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+x^{4} y^{4}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.264 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (x^{2}+1\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.605 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (y x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
{y^{\prime }}^{2} x +\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}&=a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}&=\left (x -y\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-x y^{\prime }+y \left (1-y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+4 x y y^{\prime }-5 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-5 x y y^{\prime }+6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.026 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.789 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}&=a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.289 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-y x -2 y^{2}\right ) y^{\prime }-y \left (x -y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.013 |
|
| \begin{align*}
4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| \begin{align*}
\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-4 x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
24.661 |
|
| \begin{align*}
4 x^{2} y^{2} {y^{\prime }}^{2}&=\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.608 |
|
| \begin{align*}
{y^{\prime }}^{3}-7 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.911 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.942 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+y x +y^{2}\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-x^{3} y^{6}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| \begin{align*}
x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.753 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.193 |
|
| \begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.763 |
|
| \begin{align*}
\left (x^{2} y^{2}+y x \right ) y+\left (x^{2} y^{2}-1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
2.964 |
|
| \begin{align*}
\left (x^{3} y^{3}+x^{2} y^{2}+y x +1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.984 |
|
| \begin{align*}
{y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \begin{align*}
{y^{\prime }}^{2}-\frac {a^{2}}{x^{2}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| \begin{align*}
x +y+1+\left (2 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
x y y^{\prime }-y x&=y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
2 y^{3}+2 y^{2}+\left (3 x y^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| \begin{align*}
y^{3}-x y^{2}+2 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
4 x y^{3}-9 y^{2}+4 x y^{2}+\left (3 x^{2} y^{2}-6 y x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
114.151 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+x y y^{\prime }-6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \begin{align*}
{y^{\prime }}^{2} x +\left (y-1-x^{2}\right ) y^{\prime }-\left (-1+y\right ) x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
x {y^{\prime }}^{5}-y {y^{\prime }}^{4}+\left (x^{2}+1\right ) {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.572 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| \begin{align*}
y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-3 x y y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2} a^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.172 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.220 |
|
| \begin{align*}
y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.300 |
|
| \begin{align*}
\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| \begin{align*}
-y^{2}+{y^{\prime }}^{2} x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-5 x y y^{\prime }+6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+x y^{\prime }-y^{2}-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
{y^{\prime }}^{2} x +\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (y x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \begin{align*}
{y^{\prime }}^{2}-x^{2} y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.389 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.786 |
|
| \begin{align*}
\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.516 |
|
| \begin{align*}
\left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.101 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.276 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.128 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+y x -x^{2}\right ) y^{\prime }+y \left (-x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.837 |
|
| \begin{align*}
x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.998 |
|
| \begin{align*}
x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
6 {y^{\prime }}^{2} x -\left (3 x +2 y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.882 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (x^{2}+1\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.513 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}&=\left (x -y\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.506 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.151 |
|
| \begin{align*}
\frac {y^{\prime }}{x +y}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.122 |
|
| \begin{align*}
y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| \begin{align*}
y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.055 |
|
| \begin{align*}
a y y^{\prime \prime }+b y&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.079 |
|
| \begin{align*}
a \sin \left (x \right ) y x y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.165 |
|
| \begin{align*}
f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi &=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.172 |
|
| \begin{align*}
y y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.145 |
|
| \begin{align*}
x y y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.155 |
|
| \begin{align*}
x y \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
\pi y \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.294 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
y^{3} {y^{\prime \prime }}^{2}+y y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
8.245 |
|
| \begin{align*}
y {y^{\prime \prime }}^{3}+y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
56.648 |
|
| \begin{align*}
y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
80.707 |
|
| \begin{align*}
2 y^{3} y^{\prime }+x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.818 |
|
| \begin{align*}
\left (2 x y^{3}+y\right ) y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| \begin{align*}
\left (3 x y^{3}-4 y x +y\right ) y^{\prime }+y^{2} \left (y^{2}-2\right )&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
1.101 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (b x +a y\right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \begin{align*}
{y^{\prime }}^{2}+y \left (-x +y\right ) y^{\prime }-x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+4 x y y^{\prime }-5 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+\left (x^{2} y-2 y x +x^{3}\right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+\left (y^{3} a \,x^{2}+b \right ) y^{\prime }+a b y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.225 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (-x +y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.968 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.673 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{3}+b x \left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+y^{\prime }+b x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| \begin{align*}
{y^{\prime }}^{3} \sin \left (x \right )-\left (y \sin \left (x \right )-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+y \sin \left (x \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.693 |
|
| \begin{align*}
2 y {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2 x y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.709 |
|
| \begin{align*}
x \left (a y^{\prime }+b y^{\prime \prime }+c y^{\prime \prime \prime }+e y^{\prime \prime \prime \prime }\right ) y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.217 |
|
| \begin{align*}
2 y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.230 |
|
| \begin{align*}
\left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+B x y+\left (A b +k \right ) y+B b x +b k \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
y+2 x y^{2}-x^{2} y^{3}+2 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
y^{2} \left (3 y-6 x y^{\prime }\right )-x \left (y-2 x y^{\prime }\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.428 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.001 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 \left (y x +2 y^{\prime }\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-\left (x -1\right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
x^{3}+3 t x^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.305 |
|
| \begin{align*}
x+3 t x^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.701 |
|
| \begin{align*}
y^{2} {\mathrm e}^{2 x}+\left (y \,{\mathrm e}^{2 x}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.607 |
|
| \begin{align*}
8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
198.453 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.180 |
|
| \begin{align*}
{y^{\prime }}^{2}&=9 y^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
{y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.044 |
|
| \begin{align*}
y&=y y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x^{6} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
{\mathrm e}^{x y^{2}-x^{2}} \left (y^{2}-2 x \right )+2 \,{\mathrm e}^{x y^{2}-x^{2}} x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| \begin{align*}
2 y^{3}+\left (4 x^{3} y^{3}-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
76.178 |
|
| \begin{align*}
x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
0.519 |
|
| \begin{align*}
y \cos \left (y t \right )+t \cos \left (y t \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.238 |
|
| \begin{align*}
3 t y^{2}+y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
y^{2}+2 t y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.214 |
|
| \begin{align*}
-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \begin{align*}
2 t y^{2}+2 t^{2} y y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
2 t +2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| \begin{align*}
\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+y t&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.263 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x y^{\prime }-8 x^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
{y^{\prime }}^{3}&=y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| \begin{align*}
\left (y^{\prime }-1\right )^{2}&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.490 |
|
| \begin{align*}
{y^{\prime }}^{4}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.269 |
|
| \begin{align*}
2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
\frac {y^{\prime }}{-\sin \left (y\right )+\frac {x}{y}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| \begin{align*}
y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.256 |
|
| \begin{align*}
\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
{\mathrm e}^{x^{2} y} \left (1+2 x^{2} y\right )+x^{3} {\mathrm e}^{x^{2} y} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \begin{align*}
3 x t^{2}-x t +\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
\left (x^{2}-2 y x \right ) y^{\prime }+x^{2}-3 y x +2 y^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
y \left (y x +2 x^{2} y^{2}\right )+x \left (y x -x^{2} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| \begin{align*}
\left (x^{3} y^{3}+x^{2} y^{2}+y x +1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 {y^{\prime }}^{2} x -y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| \begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| \begin{align*}
4 y^{2} {y^{\prime }}^{2}+2 \left (1+3 x \right ) x y y^{\prime }+3 x^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \begin{align*}
{y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \begin{align*}
x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.017 |
|
| \begin{align*}
{y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.215 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \begin{align*}
\left (x^{4} y^{4}+x^{2} y^{2}+y x \right ) y+\left (x^{4} y^{4}-x^{2} y^{2}+y x \right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.545 |
|
| \begin{align*}
y \left (y x +2 x^{2} y^{2}\right )+x \left (y x -x^{2} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.598 |
|
| \begin{align*}
{y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.259 |
|
| \begin{align*}
{y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.267 |
|
| \begin{align*}
{y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.267 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-3 x^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| \begin{align*}
y^{\prime } \left (y^{\prime }-y\right )&=x \left (x +y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
x +y {y^{\prime }}^{2}&=\left (y x +1\right ) y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
{y^{\prime }}^{2} x +\left (-x +y\right ) y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
{y^{\prime }}^{2}+x y^{\prime }+y y^{\prime }+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.515 |
|
| \begin{align*}
{y^{\prime }}^{3}-y^{\prime } \left (x^{2}+y x +y^{2}\right )+x y \left (x +y\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
\left (y^{\prime }+y+x \right ) \left (x y^{\prime }+x +y\right ) \left (y^{\prime }+2 x \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{3}+y \left (x^{2} y+1\right ) {y^{\prime }}^{2}+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
16.929 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+x y y^{\prime }-6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 {y^{\prime }}^{2} x -y^{2} {y^{\prime }}^{2}-2 x y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (x \cos \left (x \right )-4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+\sin \left (2 x \right ) x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.027 |
|
| \begin{align*}
\left ({y^{\prime }}^{2}-\frac {1}{a^{2}-x^{2}}\right ) \left (y^{\prime }-\sqrt {\frac {y}{x}}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.727 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (y+2 x -{\mathrm e}^{x -y}\right ) {y^{\prime }}^{2}+\left (2 y x -2 x \,{\mathrm e}^{x -y}-y \,{\mathrm e}^{x -y}\right ) y^{\prime }+2 x y \,{\mathrm e}^{x -y}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
\left (x^{3} y^{3}+x^{2} y^{2}+y x +1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.010 |
|
| \begin{align*}
x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| \begin{align*}
y^{2}+\left (y x +3 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
0.542 |
|
| \begin{align*}
y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.523 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+4 x y y^{\prime }+3 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.535 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.146 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (y x +x +y^{2}\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
0.744 |
|
| \begin{align*}
\left ({y^{\prime }}^{2}-y^{2}\right ) {\mathrm e}^{y^{\prime }}-{y^{\prime }}^{2} x +x y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.527 |
|
| \begin{align*}
{\mathrm e}^{x} \sec \left (y\right )+\left (1+{\mathrm e}^{x}\right ) \sec \left (y\right ) \tan \left (y\right ) y^{\prime }&=0 \\
y \left (3\right ) &= \frac {\pi }{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
1.434 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \begin{align*}
\left (x^{2} y^{2}-y x -2\right ) x y^{\prime }+\left (x^{2} y^{2}-1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.701 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{2}+\left (x^{3}+x y^{2}-y^{3}\right ) y^{\prime }+x^{3}-y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.748 |
|
| \begin{align*}
\left (x^{2}-2 y x \right ) {y^{\prime }}^{2}-\left (3 x^{2}+2 y\right ) \left (x -2 y\right ) y^{\prime }+6 x y \left (x -2 y\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y y^{\prime }&=-{y^{\prime }}^{2} x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
x -{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
{y^{\prime }}^{3}+y {y^{\prime }}^{2}-x^{2} y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \begin{align*}
x y^{2}-x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
y x +y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.216 |
|
| \begin{align*}
x \,{\mathrm e}^{y x}+y \,{\mathrm e}^{y x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.607 |
|
| \begin{align*}
3 x^{2} y^{2}+\left (2 x^{3} y+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
y^{2}+x y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \begin{align*}
2 y x +y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
x y^{2}+\left (x^{2} y^{2}+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.187 |
|
| \begin{align*}
x y^{2}+x^{2} y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.235 |
|
| \begin{align*}
3 x^{2} y^{2}+\left (2 x^{3} y+x^{3} y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.105 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| \begin{align*}
\left (y^{\prime }-2 x \right ) \left (y^{\prime }-3 x^{2}\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \begin{align*}
\left (y^{2}+2 y x \right ) \left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
\left (y^{2}+2 y x \right ) \left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.236 |
|
| \begin{align*}
y y^{\prime }&=x^{3} y^{2}+x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{2} y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.695 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+x y^{\prime }-y^{2}-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-7 x y y^{\prime }+12 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 \left (2 x +y\right ) y^{\prime }+8 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.367 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (y x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
{y^{\prime }}^{2}-x^{2} y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| \begin{align*}
{y^{\prime }}^{2} x +\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \begin{align*}
\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.008 |
|
| \begin{align*}
\left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.385 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 x^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.634 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+y x -x^{2}\right ) y^{\prime }+y \left (-x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.529 |
|
| \begin{align*}
x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.487 |
|
| \begin{align*}
x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.613 |
|
| \begin{align*}
6 {y^{\prime }}^{2} x -\left (3 x +2 y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (x^{2}+1\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-\left (x -y\right )^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| \begin{align*}
y^{3} \sin \left (2 x \right )-3 y^{2} \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
2 x y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
\left (x y^{\prime }+y\right )^{2}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
{y^{\prime }}^{3}-y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime }-6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.221 |
|
| \begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+2 x y y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
80.839 |
|
| \begin{align*}
\left (x^{3} y^{3}+x^{2} y^{2}+y x +1\right ) y+\left (x^{3} y^{3}-x^{2} y^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
{y^{\prime }}^{3}-y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{2}&=y y^{\prime } \left (y^{\prime }+1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
{y^{\prime }}^{2}+y x&=x y^{\prime }+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.508 |
|
| \begin{align*}
x y^{\prime } \left (x y^{\prime }+y\right )&=2 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.509 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x y^{\prime }&=8 x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
{y^{\prime }}^{2}+4 x y^{\prime }-y^{2}-2 x^{2} y&=x^{4}-4 x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
{y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \begin{align*}
y^{2}+x^{2} {y^{\prime }}^{5}&=x y \left ({y^{\prime }}^{2}+{y^{\prime }}^{3}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.825 |
|
| \begin{align*}
y^{\prime \prime \prime } {y^{\prime }}^{2}&={y^{\prime \prime \prime }}^{3} \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|