Number of problems in this table is 30
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) |
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.774 |
|
|
\[ {}2 x^{2} \left (x^{2}+x +1\right ) y^{\prime \prime }+x \left (5 x^{2}+3 x +3\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.304 |
|
|
\[ {}\sin \left (t \right ) y^{\prime \prime }+\cos \left (t \right ) y^{\prime }+\frac {y}{t} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
22.459 |
|
|
\[ {}t^{3} y^{\prime \prime }+\sin \left (t^{3}\right ) y^{\prime }+t y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
10.746 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t +1\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.225 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +12\right ) y = x^{2}+x \] |
1 |
1 |
1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.238 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y = -1+x \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.684 |
|
|
\[ {}x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{\left (-x^{2}+1\right )^{2}}+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.875 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+5 y \,{\mathrm e}^{2 x} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.15 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (1-x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.365 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (-2 x^{5}+9 x \right ) y^{\prime }+\left (10 x^{4}+5 x^{2}+25\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
13.138 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.945 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {9}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.938 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}+\frac {25}{4}\right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.287 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.003 |
|
|
\[ {}x^{2} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.051 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (-3 x^{2}+x \right ) y^{\prime }+{\mathrm e}^{x} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.393 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \,{\mathrm e}^{x} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.501 |
|
|
\[ {}x^{3} y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.432 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\left (2+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
16.607 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.891 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x^{2} y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.754 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.414 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (\cos \left (x \right )-1\right ) y^{\prime }+{\mathrm e}^{x} y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
16.961 |
|
|
\[ {}x^{2} y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.102 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.525 |
|
|
\[ {}\left (x^{3}+x^{2}\right ) y^{\prime \prime }+\left (x^{2}-2 x \right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.46 |
|
|
\[ {}x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{-2+x}+\frac {2 y}{2+x} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.737 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{\left (x -3\right )^{2}}+\frac {y}{\left (x -4\right )^{2}} = 0 \] |
1 |
1 |
1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.844 |
|
|
\[ {}x^{2} y^{\prime \prime }+6 y = 0 \] |
1 |
1 |
1 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.183 |
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