| # |
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] |
✓ |
✓ |
✓ |
✗ |
0.412 |
|
| \begin{align*}
6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.381 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
0.415 |
|
| \begin{align*}
6 x y^{3}+2 y^{4}+\left (9 y^{2} x^{2}+8 x y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.359 |
|
| \begin{align*}
2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \begin{align*}
6 y^{2} x^{2}+4 y y^{\prime } x^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.152 |
|
| \begin{align*}
14 x^{2} y^{3}+21 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.127 |
|
| \begin{align*}
\left (x +y\right )^{2}+\left (x +y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.112 |
|
| \begin{align*}
2 y^{3}+3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
0.899 |
|
| \begin{align*}
y^{4} x^{4}+x^{5} y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.240 |
|
| \begin{align*}
2 t y^{3}+3 t^{2} y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
4 y^{2}&=x^{2} {y^{\prime }}^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.262 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+y y^{\prime } x -2 x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
y^{2}-2 y y^{\prime } x +{y^{\prime }}^{2} \left (x^{2}-1\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.263 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.193 |
|
| \begin{align*}
{y^{\prime }}^{2}-3 y^{\prime }+2&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.230 |
|
| \begin{align*}
x +\left (2-x +2 y\right ) y^{\prime }&=x y \left (y^{\prime }-1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.214 |
|
| \begin{align*}
y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.263 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
\left (\sin \left (y\right )^{2}+x \cot \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
7.811 |
|
| \begin{align*}
\left (1-y^{2} x^{2}\right ) y^{\prime }&=\left (y x +1\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| \begin{align*}
x \left (-y x +1\right ) \left (1-y^{2} x^{2}\right ) y^{\prime }+\left (y x +1\right ) \left (y^{2} x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.854 |
|
| \begin{align*}
{y^{\prime }}^{2}&=y^{2} a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.556 |
|
| \begin{align*}
{y^{\prime }}^{2}&=y^{2} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
{y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.266 |
|
| \begin{align*}
{y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -3 x^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y^{\prime } x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
y y^{\prime }+{y^{\prime }}^{2}&=x \left (x +y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.937 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.959 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.436 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.517 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+y^{4} x^{4}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.522 |
|
| \begin{align*}
x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.467 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}&=a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-y^{\prime } x +y \left (1-y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x -5 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.463 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x +6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.256 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x -y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.759 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.693 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.739 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.945 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}&=a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.885 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.964 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.554 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
4.096 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
2.120 |
|
| \begin{align*}
\left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 y y^{\prime } x -4 x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
19.163 |
|
| \begin{align*}
4 y^{2} {y^{\prime }}^{2} x^{2}&=\left (x^{2}+y^{2}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.372 |
|
| \begin{align*}
{y^{\prime }}^{3}-7 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.385 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
5.279 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (2 x +y^{2}\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] |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (y^{4}+x y^{2}+x^{2}\right ) {y^{\prime }}^{2}+x y^{2} \left (y^{4}+x y^{2}+x^{2}\right ) y^{\prime }-x^{3} y^{6}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.763 |
|
| \begin{align*}
{y^{\prime }}^{3} x -\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.625 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
3.721 |
|
| \begin{align*}
\left (y^{2} x^{2}+y x \right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
2.122 |
|
| \begin{align*}
\left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.965 |
|
| \begin{align*}
{y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
{y^{\prime }}^{2}-\frac {a^{2}}{x^{2}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| \begin{align*}
x +y+1+\left (2 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.232 |
|
| \begin{align*}
y y^{\prime } x -y x&=y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
2 y^{3}+2 y^{2}+\left (3 x y^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
7.251 |
|
| \begin{align*}
y^{3}-x y^{2}+2 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
4 x y^{3}-9 y^{2}+4 x y^{2}+\left (3 y^{2} x^{2}-6 y x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
262.773 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+y y^{\prime } x -6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (y-1-x^{2}\right ) y^{\prime }-\left (-1+y\right ) x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.555 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
1.278 |
|
| \begin{align*}
\left (-x +y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-3 y y^{\prime } x +2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2} a^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.939 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \begin{align*}
y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| \begin{align*}
-y^{2}+x^{2} {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x +6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.579 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2} x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.138 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.010 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
34.119 |
|
| \begin{align*}
\left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.457 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.936 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
54.440 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
11.533 |
|
| \begin{align*}
x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+y^{2} x^{2}+y^{4}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.743 |
|
| \begin{align*}
{y^{\prime }}^{3} x -\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.738 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.675 |
|
| \begin{align*}
x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}&=\left (x -y\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.257 |
|
| \begin{align*}
\frac {y^{\prime }}{x +y}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.240 |
|
| \begin{align*}
y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \begin{align*}
y^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
a y y^{\prime \prime }+b y&=0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
a \sin \left (x \right ) y x y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.362 |
|
| \begin{align*}
f \left (x \right ) \sin \left (x \right ) y x y^{\prime } \pi &=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
y y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.248 |
|
| \begin{align*}
y y^{\prime } x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.253 |
|
| \begin{align*}
x y \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \begin{align*}
\pi y \sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.624 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.300 |
|
| \begin{align*}
y^{3} {y^{\prime \prime }}^{2}+y y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
14.307 |
|
| \begin{align*}
y {y^{\prime \prime }}^{3}+y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
116.431 |
|
| \begin{align*}
y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
158.227 |
|
| \begin{align*}
2 y^{3} y^{\prime }+x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✗ |
1.068 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (a y+b x \right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.632 |
|
| \begin{align*}
{y^{\prime }}^{2}+y \left (-x +y\right ) y^{\prime }-x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x -5 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+\left (x^{3}+x^{2} y-2 y x \right ) y^{\prime }+\left (y^{2}-x^{2} y\right ) \left (1-x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+\left (y^{3} a \,x^{2}+b \right ) y^{\prime }+a b y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.970 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.294 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (-x +y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.914 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.027 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{2}-2 y^{3} y^{\prime }+2 x y^{2}-x^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.901 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| \begin{align*}
{y^{\prime }}^{3} \sin \left (x \right )-\left (\sin \left (x \right ) y-\cos \left (x \right )^{2}\right ) {y^{\prime }}^{2}-\left (y \cos \left (x \right )^{2}+\sin \left (x \right )\right ) y^{\prime }+\sin \left (x \right ) y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.231 |
|
| \begin{align*}
2 y {y^{\prime }}^{3}-y {y^{\prime }}^{2}+2 y^{\prime } x -x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.156 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.622 |
|
| \begin{align*}
2 y^{\prime \prime \prime } y^{\prime }-3 {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
\left (A x y+B \,x^{2}+k x \right ) y^{\prime }&=A y^{2}+B y x +\left (A b +k \right ) y+B b x +b k \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
y^{2} \left (3 y-6 y^{\prime } x \right )-x \left (y-2 y^{\prime } x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
x^{3} y-y^{4}+\left (x y^{3}-x^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.455 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.297 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (2 x +y^{2}\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] |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-2 \left (y x +2 y^{\prime }\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-\left (-1+x \right )^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
x^{3}+3 t x^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
x+3 t x^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.923 |
|
| \begin{align*}
y^{2} {\mathrm e}^{2 x}+\left ({\mathrm e}^{2 x} y-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.666 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
227.826 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.066 |
|
| \begin{align*}
{y^{\prime }}^{2}&=9 y^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \begin{align*}
{y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.312 |
|
| \begin{align*}
y&=y y^{\prime }+y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x^{6} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.943 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
343.280 |
|
| \begin{align*}
x y^{2}+\left (x^{2} y+10 y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
1.136 |
|
| \begin{align*}
y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \begin{align*}
3 t y^{2}+y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
y^{2}+2 t y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.261 |
|
| \begin{align*}
-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
2 t y^{2}+2 t^{2} y y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
2 t +2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.165 |
|
| \begin{align*}
\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.878 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x -8 x^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \begin{align*}
{y^{\prime }}^{3}&=y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.015 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| \begin{align*}
\left (y^{\prime }-1\right )^{2}&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \begin{align*}
{y^{\prime }}^{4}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.111 |
|
| \begin{align*}
2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
\frac {y^{\prime }}{-\sin \left (y\right )+\frac {x}{y}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.202 |
|
| \begin{align*}
5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.782 |
|
| \begin{align*}
y+y \cos \left (y x \right )+\left (x +x \cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.363 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.058 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.417 |
|
| \begin{align*}
3 t^{2} x-t x+\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.531 |
|
| \begin{align*}
\left (-2 y x +x^{2}\right ) y^{\prime }+x^{2}-3 y x +2 y^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y \left (y x +2 y^{2} x^{2}\right )+x \left (y x -y^{2} x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.543 |
|
| \begin{align*}
\left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
4.363 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.713 |
|
| \begin{align*}
{y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.240 |
|
| \begin{align*}
{y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
5.721 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.514 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.802 |
|
| \begin{align*}
\left (y^{4} x^{4}+y^{2} x^{2}+y x \right ) y+\left (y^{4} x^{4}-y^{2} x^{2}+y x \right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.802 |
|
| \begin{align*}
y \left (y x +2 y^{2} x^{2}\right )+x \left (y x -y^{2} x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.568 |
|
| \begin{align*}
{y^{\prime }}^{2}-7 y^{\prime }+12&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
{y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
{y^{\prime }}^{2}-9 y^{\prime }+18&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y^{\prime } x -3 x^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
y^{\prime } \left (y^{\prime }-y\right )&=x \left (x +y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.476 |
|
| \begin{align*}
x +y {y^{\prime }}^{2}&=\left (y x +1\right ) y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (-x +y\right ) y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{\prime } x +y y^{\prime }+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.277 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
\left (y^{\prime }+y+x \right ) \left (y^{\prime } x +x +y\right ) \left (y^{\prime }+2 x \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.823 |
|
| \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] |
✓ |
✓ |
✗ |
✗ |
49.794 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+y y^{\prime } x -6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 x {y^{\prime }}^{2}-y^{2} {y^{\prime }}^{2}-2 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (\cos \left (x \right ) x -4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+\sin \left (2 x \right ) x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.772 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
5.733 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.890 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \begin{align*}
\left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \begin{align*}
{y^{\prime }}^{3}-\left (x^{2}+y x +y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+y^{2} x^{2}+x^{3} y\right ) y^{\prime }-x^{3} y^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
2.060 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
4.853 |
|
| \begin{align*}
x y^{2} \left ({y^{\prime }}^{2}+2\right )&=2 y^{3} y^{\prime }+x^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.666 |
|
| \begin{align*}
y^{2}+\left (y x +3 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
48.458 |
|
| \begin{align*}
y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
y^{\prime } \left (y^{\prime }+y\right )&=x \left (x +y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.655 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x +3 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.882 |
|
| \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‘]] |
✓ |
✓ |
✗ |
✗ |
1.035 |
|
| \begin{align*}
\left ({y^{\prime }}^{2}-y^{2}\right ) {\mathrm e}^{y^{\prime }}-x {y^{\prime }}^{2}+x y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.156 |
|
| \begin{align*}
{\mathrm e}^{x} \sec \left (y\right )+\left ({\mathrm e}^{x}+1\right ) \sec \left (y\right ) \tan \left (y\right ) y^{\prime }&=0 \\
y \left (3\right ) &= \frac {\pi }{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
2.918 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=-x +y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| \begin{align*}
\left (y^{2} x^{2}-y x -2\right ) x y^{\prime }+y \left (y^{2} x^{2}-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.333 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
5.137 |
|
| \begin{align*}
\left (-2 y x +x^{2}\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] |
✓ |
✓ |
✓ |
✓ |
0.701 |
|
| \begin{align*}
y y^{\prime }&=-x {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
x -x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
{y^{\prime }}^{3}+y {y^{\prime }}^{2}-x^{2} y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.165 |
|
| \begin{align*}
x y^{2}-x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
y x +y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \begin{align*}
y \,{\mathrm e}^{y x}+x \,{\mathrm e}^{y x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| \begin{align*}
x \,{\mathrm e}^{y x}+y \,{\mathrm e}^{y x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \begin{align*}
3 y^{2} x^{2}+\left (2 x^{3} y+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
4.364 |
|
| \begin{align*}
y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \begin{align*}
2 y x +y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.970 |
|
| \begin{align*}
x y^{2}+\left (y^{2} x^{2}+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| \begin{align*}
x y^{2}+x^{2} y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
3 y^{2} x^{2}+\left (2 x^{3} y+x^{3} y^{4}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.822 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.558 |
|
| \begin{align*}
\left (y^{\prime }-2 x \right ) \left (y^{\prime }-3 x^{2}\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \begin{align*}
\left (y^{2}+2 y x \right ) \left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
\left (y^{2}+2 y x \right ) \left (x^{2}+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
y y^{\prime }&=x^{3} y^{2}+x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
y^{2} y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.929 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.175 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-7 y y^{\prime } x +12 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.912 |
|
| \begin{align*}
x {y^{\prime }}^{2}-2 \left (2 x +y\right ) y^{\prime }+8 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \begin{align*}
x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.751 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2} x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.981 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.289 |
|
| \begin{align*}
x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } x y \left (x +y\right )+x^{3} y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.481 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
32.239 |
|
| \begin{align*}
\left (x -y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
14.531 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.966 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2}&=4 y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
51.951 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
23.165 |
|
| \begin{align*}
x y \left (x^{2}+y^{2}\right ) \left (-1+{y^{\prime }}^{2}\right )&=y^{\prime } \left (x^{4}+y^{2} x^{2}+y^{4}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.751 |
|
| \begin{align*}
{y^{\prime }}^{3} x -\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+y x \right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.507 |
|
| \begin{align*}
6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.489 |
|
| \begin{align*}
x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.707 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-\left (x -y\right )^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \begin{align*}
x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \begin{align*}
y^{3} \sin \left (2 x \right )-3 y^{2} \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.305 |
|
| \begin{align*}
2 y y^{\prime } x +y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
\left (y^{\prime } x +y\right )^{2}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \begin{align*}
{y^{\prime }}^{3}-y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime }-6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
\left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
483.683 |
|
| \begin{align*}
\left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.135 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| \begin{align*}
{y^{\prime }}^{3}-y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.142 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{2}&=y y^{\prime } \left (1+y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.261 |
|
| \begin{align*}
{y^{\prime }}^{2}+y x&=y^{\prime } x +y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.866 |
|
| \begin{align*}
x y^{\prime } \left (y^{\prime } x +y\right )&=2 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x&=8 x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
{y^{\prime }}^{2}+4 y^{\prime } x -y^{2}-2 x^{2} y&=x^{4}-4 x^{2} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \begin{align*}
{y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.160 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
20.925 |
|
| \begin{align*}
y^{\prime \prime \prime } {y^{\prime }}^{2}&={y^{\prime \prime \prime }}^{3} \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.285 |
|