# |
ODE |
CAS classification |
Solved? |
\[
{}t x^{\prime \prime }+\left (t -2\right ) x^{\prime }+x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
\[
{}t x^{\prime \prime }+\left (3 t -1\right ) x^{\prime }+3 x = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
|
\[
{}t x^{\prime \prime }-\left (4 t +1\right ) x^{\prime }+2 \left (2 t +1\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
\[
{}t x^{\prime \prime }+2 \left (t -1\right ) x^{\prime }-2 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
\[
{}t x^{\prime \prime }-2 x^{\prime }+x t = 0
\] |
[_Lienard] |
✓ |
|
\[
{}t x^{\prime \prime }+\left (4 t -2\right ) x^{\prime }+\left (13 t -4\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
\[
{}t y^{\prime \prime }+y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
|
\[
{}x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (4 x +9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y = 3 \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✗ |
|