|
# |
ODE |
CAS classification |
Solved? |
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = y^{\prime } y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}+y^{\prime }
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = y^{\prime } y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y^{\prime \prime }+{y^{\prime }}^{2}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y y^{\prime \prime }-y^{\prime } y = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+y^{\prime } y = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime } y = 0
\] |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}x \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right ) = y^{\prime } y
\] |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}x y^{\prime \prime } = y^{\prime } \left (2-3 x y^{\prime }\right )
\] |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}3 y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+\sin \left (y\right ) {y^{\prime }}^{2} = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}10 y^{\prime \prime }+x^{2} y^{\prime }+\frac {3 {y^{\prime }}^{2}}{y} = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y^{\prime \prime }+f \left (y\right ) {y^{\prime }}^{2}+g \left (x \right ) y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}a y y^{\prime \prime }+b {y^{\prime }}^{2}-\frac {y y^{\prime }}{\sqrt {c^{2}+x^{2}}} = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime } y = 0
\] |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}x y y^{\prime \prime }+2 x {y^{\prime }}^{2}+a y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+a y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}x y y^{\prime \prime }-4 x {y^{\prime }}^{2}+4 y^{\prime } y = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}2 x y y^{\prime \prime }-x {y^{\prime }}^{2}+y^{\prime } y = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = \frac {y y^{\prime }}{\sqrt {x^{2}+1}}
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}-y^{\prime } y = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 2 y^{\prime } y
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y^{\prime \prime } = y^{\prime } \left (y^{\prime }-2\right )
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y y^{\prime \prime }+2 {y^{\prime }}^{2} = 3 y^{\prime } y
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y^{\prime \prime } = y^{\prime } \left (y^{\prime }+1\right )
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}-y^{\prime } y = 0
\] |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2}-2 y^{\prime } y = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
|