|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime }}^{2}-a y y^{\prime }-a x = 0
\] |
[_dAlembert] |
✓ |
85.914 |
|
|
\[
{}{y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y = 0
\] |
[_quadrature] |
✓ |
0.503 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime } y+y^{2} \ln \left (a y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
5.178 |
|
|
\[
{}{y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+2 x y = 0
\] |
[_quadrature] |
✓ |
0.403 |
|
|
\[
{}{y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+4+y^{2} = 0
\] |
[_quadrature] |
✓ |
1.751 |
|
|
\[
{}{y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
0.474 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{2} y^{\prime }+y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.869 |
|
|
\[
{}{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.188 |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+x^{4} y^{4} = 0
\] |
[_separable] |
✓ |
0.670 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.753 |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
1.305 |
|
|
\[
{}{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
4.230 |
|
|
\[
{}{y^{\prime }}^{2} = {\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.224 |
|
|
\[
{}2 {y^{\prime }}^{2}+y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.665 |
|
|
\[
{}2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.511 |
|
|
\[
{}2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.150 |
|
|
\[
{}2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right ) = 0
\] |
[_quadrature] |
✓ |
10.929 |
|
|
\[
{}3 {y^{\prime }}^{2}-2 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.538 |
|
|
\[
{}3 {y^{\prime }}^{2}+4 y^{\prime } x +x^{2}-y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.784 |
|
|
\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
[_quadrature] |
✓ |
0.419 |
|
|
\[
{}4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✗ |
19.778 |
|
|
\[
{}4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.267 |
|
|
\[
{}5 {y^{\prime }}^{2}+3 y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.573 |
|
|
\[
{}5 {y^{\prime }}^{2}+6 y^{\prime } x -2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.561 |
|
|
\[
{}9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
71.931 |
|
|
\[
{}x {y^{\prime }}^{2} = a
\] |
[_quadrature] |
✓ |
0.362 |
|
|
\[
{}x {y^{\prime }}^{2} = -x^{2}+a
\] |
[_quadrature] |
✓ |
0.763 |
|
|
\[
{}x {y^{\prime }}^{2} = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.093 |
|
|
\[
{}x {y^{\prime }}^{2}+x -2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.036 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } = y
\] |
[_rational, _dAlembert] |
✓ |
1.219 |
|
|
\[
{}x {y^{\prime }}^{2}+2 y^{\prime }-y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.191 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime }-y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.201 |
|
|
\[
{}x {y^{\prime }}^{2}+4 y^{\prime }-2 y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.319 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.032 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.297 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
0.627 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.544 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.106 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+x^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.366 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.830 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }-y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.249 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (-y+a \right ) y^{\prime }+b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.594 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.633 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (a +x -y\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.687 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (3 x -y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.938 |
|
|
\[
{}x {y^{\prime }}^{2}+a +b x -y-b y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
1.239 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.682 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.592 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.881 |
|
|
\[
{}x {y^{\prime }}^{2}-3 y y^{\prime }+9 x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
4.553 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
[_quadrature] |
✓ |
0.428 |
|
|
\[
{}x {y^{\prime }}^{2}-a y y^{\prime }+b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.888 |
|
|
\[
{}x {y^{\prime }}^{2}+a y y^{\prime }+b x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.506 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
0.310 |
|
|
\[
{}x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
0.366 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
0.450 |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2} = y
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
1.003 |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.654 |
|
|
\[
{}\left (a -x \right ) {y^{\prime }}^{2}+y y^{\prime }-b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.602 |
|
|
\[
{}2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.454 |
|
|
\[
{}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.069 |
|
|
\[
{}\left (3 x +1\right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.652 |
|
|
\[
{}\left (3 x +5\right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y = 0
\] |
[_rational, _dAlembert] |
✓ |
2.256 |
|
|
\[
{}4 x {y^{\prime }}^{2} = \left (a -3 x \right )^{2}
\] |
[_quadrature] |
✓ |
0.473 |
|
|
\[
{}4 x {y^{\prime }}^{2}+2 y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
35.092 |
|
|
\[
{}4 x {y^{\prime }}^{2}-3 y y^{\prime }+3 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.581 |
|
|
\[
{}4 x {y^{\prime }}^{2}+4 y y^{\prime } = 1
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.640 |
|
|
\[
{}4 x {y^{\prime }}^{2}+4 y y^{\prime }-y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.343 |
|
|
\[
{}4 \left (2-x \right ) {y^{\prime }}^{2}+1 = 0
\] |
[_quadrature] |
✓ |
0.326 |
|
|
\[
{}16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.652 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = a^{2}
\] |
[_quadrature] |
✓ |
0.424 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = y^{2}
\] |
[_separable] |
✓ |
1.368 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.000 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
1.037 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+y^{2}-y^{4} = 0
\] |
[_separable] |
✓ |
2.762 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{\prime } x +y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
0.585 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y = 0
\] |
[_rational] |
✗ |
70.604 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y^{\prime } y-x +y \left (1+y\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.488 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y^{\prime } y-x^{4}+\left (-x^{2}+1\right ) y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
9.357 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (1+2 x y\right ) y^{\prime }+1+y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.730 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (a +2 x y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.820 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.960 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+2 x \left (2 x +y\right ) y^{\prime }-4 a +y^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.612 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x \left (x^{3}-2 y\right ) y^{\prime }-\left (2 x^{3}-y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.089 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y^{\prime } y+2 y^{2} = 0
\] |
[_separable] |
✓ |
0.714 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-3 x y^{\prime } y+x^{3}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
73.167 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y^{\prime } y-5 y^{2} = 0
\] |
[_separable] |
✓ |
0.758 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y = 0
\] |
[_separable] |
✓ |
0.614 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y^{\prime } y+6 y^{2} = 0
\] |
[_separable] |
✓ |
0.682 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x \left (x^{2}+x y-2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y = 0
\] |
[_rational] |
✗ |
85.603 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (2 x +y\right ) y y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
125.585 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
74.387 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
4.462 |
|
|
\[
{}\left (-x^{2}+1\right ) {y^{\prime }}^{2} = 1-y^{2}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.356 |
|
|
\[
{}\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+4 x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
110.494 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2} = b^{2}
\] |
[_quadrature] |
✓ |
0.767 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2} = 0
\] |
[_quadrature] |
✓ |
0.503 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2} = b^{2}
\] |
[_quadrature] |
✓ |
0.382 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2} = x^{2}
\] |
[_quadrature] |
✓ |
0.453 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y^{\prime } y+x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
30.337 |
|