| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }-x +y \left (y+1\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
36.935 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }-x^{4}+\left (-x^{2}+1\right ) y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
36.586 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-\left (1+2 y x \right ) y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.494 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✓ |
16.568 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.671 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+2 x \left (2 x +y\right ) y^{\prime }-4 a +y^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
16.682 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+x \left (x^{3}-2 y\right ) y^{\prime }-\left (2 x^{3}-y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
6.138 |
|
| \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}-3 x y y^{\prime }+x^{3}+2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.302 |
|
| \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}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.483 |
|
| \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}+x \left (x^{2}+y x -2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
104.534 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
66.009 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
70.832 |
|
| \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 (-x^{2}+1\right ) {y^{\prime }}^{2}&=1-y^{2} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.690 |
|
| \begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+4 x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.934 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.271 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.779 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.782 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.937 |
|
| \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*}
\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+b +y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.241 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x^{2}-4 x y y^{\prime }&=8 x^{3}-y^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| \begin{align*}
a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+a \left (1-a \right ) x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
22.135 |
|
| \begin{align*}
\left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-a^{2} x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
62.861 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
30.126 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
35.345 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
6.336 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) {y^{\prime }}^{2}-2 \left (-x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
62.017 |
|
| \begin{align*}
4 x \left (-x +a \right ) \left (-x +b \right ) {y^{\prime }}^{2}&=\left (a b -2 x \left (a +b \right )+2 x^{2}\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.977 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
5.006 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.266 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}+x y^{2} y^{\prime }-y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
8.329 |
|
| \begin{align*}
x^{2} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.805 |
|
| \begin{align*}
3 x^{4} {y^{\prime }}^{2}-y x -y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.257 |
|
| \begin{align*}
4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
6.449 |
|
| \begin{align*}
x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
4.743 |
|
| \begin{align*}
x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
4.142 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.297 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=a^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.418 |
|
| \begin{align*}
y {y^{\prime }}^{2}&={\mathrm e}^{2 x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
20.270 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 a x y^{\prime }-a y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.316 |
|
| \begin{align*}
y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
25.589 |
|
| \begin{align*}
y {y^{\prime }}^{2}+a x y^{\prime }+b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.172 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.619 |
|
| \begin{align*}
y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.651 |
|
| \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 (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.529 |
|
| \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*}
y {y^{\prime }}^{2}+y&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.421 |
|
| \begin{align*}
\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.652 |
|
| \begin{align*}
\left (2 x -y\right ) {y^{\prime }}^{2}-2 \left (1-x \right ) y^{\prime }+2-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.314 |
|
| \begin{align*}
2 y {y^{\prime }}^{2}+\left (5-4 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.227 |
|
| \begin{align*}
9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.264 |
|
| \begin{align*}
\left (1-a y\right ) {y^{\prime }}^{2}&=a y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.937 |
|
| \begin{align*}
\left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
47.555 |
|
| \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 (a +x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
195.393 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
174.573 |
|
| \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*}
x \left (x -2 y\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-2 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
113.907 |
|
| \begin{align*}
x \left (x -2 y\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-2 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
113.648 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}&=a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.788 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.841 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
2.271 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
52.244 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.867 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.964 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a -y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.952 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.401 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+a -x^{2}+2 y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.600 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +a \,x^{2}+\left (1-a \right ) y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.895 |
|
| \begin{align*}
\left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
25.211 |
|
| \begin{align*}
\left (a^{2}-y^{2}\right ) {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| \begin{align*}
\left (a^{2} x^{2}-y^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }+x^{2} \left (a^{2}-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.899 |
|
| \begin{align*}
\left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.102 |
|
| \begin{align*}
\left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
62.863 |
|
| \begin{align*}
\left (x^{2} \left (-a^{2}+1\right )+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
15.934 |
|
| \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*}
\left (a^{2}-\left (x -y\right )^{2}\right ) {y^{\prime }}^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.021 |
|
| \begin{align*}
2 y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-1+x^{2}+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.677 |
|
| \begin{align*}
3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.691 |
|
| \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*}
9 y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.731 |
|
| \begin{align*}
\left (2-3 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.297 |
|
| \begin{align*}
\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.963 |
|
| \begin{align*}
\left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.616 |
|
| \begin{align*}
a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.180 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
11.628 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_rational] |
✗ |
✓ |
✓ |
✗ |
289.033 |
|