These are ode of order 3 or higher that are missing \(y\) solved by reduction of order. Number of problems in this table is 35
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) |
|
\[ {}x y^{\prime \prime \prime }-y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.185 |
|
|
\[ {}x y^{\prime \prime \prime }+2 y^{\prime \prime } = A x \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.451 |
|
|
\[ {}\left (2 x^{3}-1\right ) y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+6 x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
3.004 |
|
|
\[ {}y^{\left (5\right )}-\frac {y^{\prime \prime \prime \prime }}{t} = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_y]] |
✓ |
✓ |
1.342 |
|
|
\[ {}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_y]] |
✓ |
✓ |
1.242 |
|
|
\[ {}\left (2 x -1\right ) y^{\prime \prime \prime }+\left (x +4\right ) y^{\prime \prime }+2 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
5.994 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-x y^{\prime \prime }+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.652 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+5 x y^{\prime \prime }+4 y^{\prime }-\ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.429 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime }+6 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.44 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.729 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+\left (-a^{2}+1\right ) x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.444 |
|
|
\[ {}4 x^{4} y^{\prime \prime \prime }-4 x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }-1 = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.365 |
|
|
\[ {}y^{\prime \prime \prime \prime } x +5 y^{\prime \prime \prime }-24 = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.759 |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.64 |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+6 x y^{\prime \prime \prime }+6 y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.507 |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.574 |
|
|
\[ {}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.477 |
|
|
\[ {}\left (2+x \right )^{2} y^{\prime \prime \prime }+\left (2+x \right ) y^{\prime \prime }+y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.587 |
|
|
\[ {}4 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.784 |
|
|
\[ {}y^{\prime \prime \prime }+\frac {3 y^{\prime \prime }}{x} = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.71 |
|
|
\[ {}x y^{\prime \prime \prime } = 2 \] |
1 |
1 |
1 |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
0.278 |
|
|
\[ {}x y^{\prime \prime \prime }+x y^{\prime } = 4 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
15.169 |
|
|
\[ {}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.76 |
|
|
\[ {}x y^{\prime \prime \prime }+2 y^{\prime \prime } = 6 x \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.868 |
|
|
\[ {}t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.441 |
|
|
\[ {}\left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (2+t \right ) y^{\prime } = -2-t \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.491 |
|
|
\[ {}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 x y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.823 |
|
|
\[ {}x y^{\prime \prime \prime } = 2 \] |
1 |
1 |
1 |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
0.227 |
|
|
\[ {}x y^{\prime \prime \prime }-y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.553 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.47 |
|
|
\[ {}x^{2} y^{\prime \prime \prime } = 2 y^{\prime } \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.345 |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime \prime }-12 y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.564 |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.044 |
|
|
\[ {}x^{2} y^{\prime \prime \prime \prime }+4 x y^{\prime \prime \prime }+2 y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.757 |
|
|
\[ {}x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.667 |
|
|
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