These are odes of the form \(a y''+b y'+ \left (c e^{r x}-m\right ) y=0\) solved as Bessel ode using transformation \(x=\ln t\). Number of problems in this table is 10
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+{\mathrm e}^{2 x} y = n^{2} y \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.094 |
|
|
\[ {}y^{\prime \prime }+\left ({\mathrm e}^{2 x}-v^{2}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.193 |
|
|
\[ {}y^{\prime \prime }+a \,{\mathrm e}^{b x} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.22 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+a \,{\mathrm e}^{-2 x} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.664 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.569 |
|
|
\[ {}y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.382 |
|
|
\[ {}y^{\prime \prime }+\left (a \,{\mathrm e}^{x}-b \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.369 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{2 x a} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.573 |
|
|
\[ {}y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 x a} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.893 |
|
|
\[ {}y^{\prime \prime }+a y^{\prime }+\left (b \,{\mathrm e}^{\lambda x}+c \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.703 |
|
|
|
||||||||
|
|
||||||||