|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime }}^{2}-a y y^{\prime }-a x = 0
\] |
[_dAlembert] |
✓ |
116.157 |
|
|
\[
{}{y^{\prime }}^{2}+\left (a x +b y\right ) y^{\prime }+a b x y = 0
\] |
[_quadrature] |
✓ |
0.870 |
|
|
\[
{}{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.448 |
|
|
\[
{}{y^{\prime }}^{2}-\left (2 x y+1\right ) y^{\prime }+2 x y = 0
\] |
[_quadrature] |
✓ |
1.521 |
|
|
\[
{}{y^{\prime }}^{2}-\left (4+y^{2}\right ) y^{\prime }+4+y^{2} = 0
\] |
[_quadrature] |
✓ |
3.278 |
|
|
\[
{}{y^{\prime }}^{2}-\left (x -y\right ) y y^{\prime }-x y^{3} = 0
\] |
[_separable] |
✓ |
1.996 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{2} y^{\prime }+y^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.194 |
|
|
\[
{}{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.692 |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (y^{2}+x^{2}\right ) y^{\prime }+x^{4} y^{4} = 0
\] |
[_separable] |
✓ |
3.160 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.995 |
|
|
\[
{}{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2} = 0
\] |
[_separable] |
✓ |
1.099 |
|
|
\[
{}{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
4.483 |
|
|
\[
{}{y^{\prime }}^{2} = {\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.776 |
|
|
\[
{}2 {y^{\prime }}^{2}+x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.529 |
|
|
\[
{}2 {y^{\prime }}^{2}-\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.408 |
|
|
\[
{}2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 x y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.658 |
|
|
\[
{}2 {y^{\prime }}^{2}+2 \left (6 y-1\right ) y^{\prime }+3 y \left (6 y-1\right ) = 0
\] |
[_quadrature] |
✓ |
3.014 |
|
|
\[
{}3 {y^{\prime }}^{2}-2 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.371 |
|
|
\[
{}3 {y^{\prime }}^{2}+4 x y^{\prime }+x^{2}-y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.504 |
|
|
\[
{}4 {y^{\prime }}^{2} = 9 x
\] |
[_quadrature] |
✓ |
0.251 |
|
|
\[
{}4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
9.411 |
|
|
\[
{}4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.886 |
|
|
\[
{}5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.410 |
|
|
\[
{}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.454 |
|
|
\[
{}9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
80.854 |
|
|
\[
{}x {y^{\prime }}^{2} = a
\] |
[_quadrature] |
✓ |
0.234 |
|
|
\[
{}x {y^{\prime }}^{2} = -x^{2}+a
\] |
[_quadrature] |
✓ |
0.481 |
|
|
\[
{}x {y^{\prime }}^{2} = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.392 |
|
|
\[
{}x {y^{\prime }}^{2}+x -2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.849 |
|
|
\[
{}x {y^{\prime }}^{2}+y^{\prime } = y
\] |
[_rational, _dAlembert] |
✓ |
0.895 |
|
|
\[
{}x {y^{\prime }}^{2}+2 y^{\prime }-y = 0
\] |
[_rational, _dAlembert] |
✓ |
0.890 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y^{\prime }-y = 0
\] |
[_rational, _dAlembert] |
✓ |
0.887 |
|
|
\[
{}x {y^{\prime }}^{2}+4 y^{\prime }-2 y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.070 |
|
|
\[
{}x {y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.788 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.512 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
0.486 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.375 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.040 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }+x^{3} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.474 |
|
|
\[
{}x {y^{\prime }}^{2}-y y^{\prime }+a y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.819 |
|
|
\[
{}x {y^{\prime }}^{2}+y y^{\prime }-y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
15.436 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (-y+a \right ) y^{\prime }+b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.495 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.526 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (a +x -y\right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.569 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (3 x -y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.673 |
|
|
\[
{}x {y^{\prime }}^{2}+a +b x -y-b y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
1.116 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.504 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+a x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.508 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.707 |
|
|
\[
{}x {y^{\prime }}^{2}-3 y y^{\prime }+9 x^{2} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
6.117 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
[_quadrature] |
✓ |
2.004 |
|
|
\[
{}x {y^{\prime }}^{2}-a y y^{\prime }+b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.638 |
|
|
\[
{}x {y^{\prime }}^{2}+a y y^{\prime }+b x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.026 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
1.191 |
|
|
\[
{}x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
2.388 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
1.387 |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2} = y
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.716 |
|
|
\[
{}\left (x +1\right ) {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.575 |
|
|
\[
{}\left (-x +a \right ) {y^{\prime }}^{2}+y y^{\prime }-b = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.512 |
|
|
\[
{}2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.098 |
|
|
\[
{}3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.460 |
|
|
\[
{}\left (3 x +1\right ) {y^{\prime }}^{2}-3 \left (y+2\right ) y^{\prime }+9 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.562 |
|
|
\[
{}\left (5+3 x \right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y = 0
\] |
[_rational, _dAlembert] |
✓ |
2.182 |
|
|
\[
{}4 x {y^{\prime }}^{2} = \left (a -3 x \right )^{2}
\] |
[_quadrature] |
✓ |
0.291 |
|
|
\[
{}4 x {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.245 |
|
|
\[
{}4 x {y^{\prime }}^{2}-3 y y^{\prime }+3 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.487 |
|
|
\[
{}4 x {y^{\prime }}^{2}+4 y y^{\prime } = 1
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
0.499 |
|
|
\[
{}4 x {y^{\prime }}^{2}+4 y y^{\prime }-y^{4} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
15.424 |
|
|
\[
{}4 \left (2-x \right ) {y^{\prime }}^{2}+1 = 0
\] |
[_quadrature] |
✓ |
0.226 |
|
|
\[
{}16 x {y^{\prime }}^{2}+8 y y^{\prime }+y^{6} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.424 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = a^{2}
\] |
[_quadrature] |
✓ |
0.385 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = y^{2}
\] |
[_separable] |
✓ |
2.663 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x^{2}-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.385 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
2.872 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+y^{2}-y^{4} = 0
\] |
[_separable] |
✓ |
2.182 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-x y^{\prime }+y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
2.539 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y = 0
\] |
[_rational] |
✓ |
85.112 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x +y \left (1+y\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.471 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{4}+\left (-x^{2}+1\right ) y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
9.206 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (2 x y+1\right ) y^{\prime }+1+y^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.636 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (a +2 x y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
0.671 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.661 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+2 x \left (2 x +y\right ) y^{\prime }-4 a +y^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
4.290 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x \left (x^{3}-2 y\right ) y^{\prime }-\left (2 x^{3}-y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.176 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
2.952 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+x^{3}+2 y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
73.020 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2} = 0
\] |
[_separable] |
✓ |
2.744 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-4 x \left (y+2\right ) y^{\prime }+4 \left (y+2\right ) y = 0
\] |
[_separable] |
✓ |
0.744 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
3.003 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x \left (x^{2}+x y-2 y\right ) y^{\prime }+\left (1-x \right ) \left (x^{2}-y\right ) y = 0
\] |
[_rational] |
✓ |
78.914 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (2 x +y\right ) y y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
148.817 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
151.102 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+\left (a +b \,x^{2} y^{3}\right ) y^{\prime }+a b y^{3} = 0
\] |
[_quadrature] |
✓ |
1.015 |
|
|
\[
{}\left (-x^{2}+1\right ) {y^{\prime }}^{2} = 1-y^{2}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.000 |
|
|
\[
{}\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+4 x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
44.562 |
|
|
\[
{}\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2} = b^{2}
\] |
[_quadrature] |
✓ |
0.556 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2} = 0
\] |
[_quadrature] |
✓ |
0.335 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2} = b^{2}
\] |
[_quadrature] |
✓ |
0.372 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2} = x^{2}
\] |
[_quadrature] |
✓ |
0.273 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
27.424 |
|