| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x +y \left (1+y\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
24.304 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{4}+y^{2} \left (-x^{2}+1\right )&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
16.487 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-\left (2 y x +1\right ) y^{\prime }+1+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.403 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-\left (a +2 y x \right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✓ |
22.384 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.407 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{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)]‘]] |
✓ |
✓ |
✓ |
✗ |
9.388 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+x \left (x^{3}-2 y\right ) y^{\prime }-\left (2 x^{3}-y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
4.141 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+3 y y^{\prime } x +2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.541 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-3 y y^{\prime } x +x^{3}+2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.801 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x -5 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.992 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}-5 y y^{\prime } x +6 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{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] |
✗ |
✗ |
✗ |
✗ |
97.898 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+\left (2 x +y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
102.123 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
102.428 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.521 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.832 |
|
| \begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +4 x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.785 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.780 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.318 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.723 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 y y^{\prime } x +x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.807 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x -y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +b +y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.558 |
|
| \begin{align*}
4 x^{2} {y^{\prime }}^{2}-4 y y^{\prime } x&=8 x^{3}-y^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.349 |
|
| \begin{align*}
a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+x^{2} a \left (1-a \right )+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
19.016 |
|
| \begin{align*}
\left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -a^{2} x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
70.048 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.309 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
36.164 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
4.311 |
|
| \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)]‘]] |
✗ |
✓ |
✓ |
✗ |
50.306 |
|
| \begin{align*}
4 x \left (a -x \right ) \left (b -x \right ) {y^{\prime }}^{2}&=\left (a b -2 \left (a +b \right ) x +2 x^{2}\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}-y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.505 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}+2 y y^{\prime } x^{3}-4&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.555 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}+y^{\prime } y^{2} x -y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
13.399 |
|
| \begin{align*}
x^{2} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.564 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
10.680 |
|
| \begin{align*}
4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
4.382 |
|
| \begin{align*}
x^{6} {y^{\prime }}^{2}-2 y^{\prime } x -4 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.400 |
|
| \begin{align*}
x^{8} {y^{\prime }}^{2}+3 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
3.399 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.749 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=a^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.772 |
|
| \begin{align*}
y {y^{\prime }}^{2}&={\mathrm e}^{2 x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
45.388 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 a x y^{\prime }-a y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.462 |
|
| \begin{align*}
y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.408 |
|
| \begin{align*}
y {y^{\prime }}^{2}+a x y^{\prime }+b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.808 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.333 |
|
| \begin{align*}
y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.670 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.741 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.328 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
y {y^{\prime }}^{2}+y&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.869 |
|
| \begin{align*}
\left (x +y\right ) {y^{\prime }}^{2}+2 y^{\prime } x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.655 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
1.868 |
|
| \begin{align*}
2 y {y^{\prime }}^{2}+\left (5-4 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.635 |
|
| \begin{align*}
9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.575 |
|
| \begin{align*}
\left (1-a y\right ) {y^{\prime }}^{2}&=a y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.400 |
|
| \begin{align*}
\left (x^{2}-a y\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
45.613 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.394 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.709 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (a +x^{2}-y^{2}\right ) y^{\prime }-y x&=0 \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
224.296 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (a -b \,x^{2}+y^{2}\right ) y^{\prime }-b x y&=0 \\
\end{align*} |
[_rational] |
✓ |
✗ |
✓ |
✗ |
199.068 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (3 x^{2}-2 y^{2}\right ) y^{\prime }-6 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.502 |
|
| \begin{align*}
x \left (x -2 y\right ) {y^{\prime }}^{2}-2 y y^{\prime } x -2 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
155.869 |
|
| \begin{align*}
x \left (x -2 y\right ) {y^{\prime }}^{2}+6 y y^{\prime } x -2 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
139.359 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}&=a^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.308 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-a^{2}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.242 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-3 y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.546 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
45.634 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.076 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-\left (x +1\right ) y y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.510 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+2 y y^{\prime } x +x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.842 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+2 y y^{\prime } x +a -y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.796 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.827 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +a -x^{2}+2 y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.286 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (-1+a \right ) b +a \,x^{2}+\left (1-a \right ) y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.407 |
|
| \begin{align*}
\left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
29.613 |
|
| \begin{align*}
\left (a^{2}-y^{2}\right ) {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.045 |
|
| \begin{align*}
\left (a^{2} x^{2}-y^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +x^{2} \left (a^{2}-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.354 |
|
| \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‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.900 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
62.148 |
|
| \begin{align*}
\left (\left (-a^{2}+1\right ) x^{2}+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] |
✓ |
✓ |
✓ |
✗ |
17.223 |
|
| \begin{align*}
\left (x +y\right )^{2} {y^{\prime }}^{2}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.673 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
3.340 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
17.524 |
|
| \begin{align*}
2 y^{2} {y^{\prime }}^{2}+2 y y^{\prime } x -1+x^{2}+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.306 |
|
| \begin{align*}
3 y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+4 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.395 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.594 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✗ |
12.923 |
|
| \begin{align*}
9 y^{2} {y^{\prime }}^{2}-3 y^{\prime } x +y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.402 |
|
| \begin{align*}
\left (2-3 y\right )^{2} {y^{\prime }}^{2}&=4-4 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
10.272 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.778 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
19.511 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
6.810 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_rational] |
✗ |
✓ |
✓ |
✗ |
258.590 |
|