| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=\cos \left (2 x \right ) \\
y \left (0\right ) &= {\frac {1}{25}} \\
y \left (\pi \right ) &= {\frac {1}{25}} \\
y^{\prime }\left (0\right ) &= {\frac {2}{15}} \\
y^{\prime }\left (\pi \right ) &= {\frac {2}{25}} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
2 y^{\prime \prime }+4 x y^{\prime \prime \prime }+x^{2} y^{\prime \prime \prime \prime }&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[[_high_order, _missing_y]] |
✗ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
6 x y^{\prime \prime }+6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[[_high_order, _missing_y]] |
✗ |
✗ |
✗ |
✗ |
0.517 |
|
| \begin{align*}
y^{\prime }-2 y x&=0 \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.487 |
|
| \begin{align*}
4 x y^{\prime }+2 y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✗ |
0.298 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-n y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
9 x \left (1-x \right ) y^{\prime \prime }-12 y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✓ |
0.722 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }+y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.260 |
|
| \begin{align*}
y^{\prime \prime }-\left (x^{2}+1\right ) y&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.264 |
|
| \begin{align*}
y^{\prime \prime }&=x^{2} y-y^{\prime } \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
y^{\prime \prime }-y \,{\mathrm e}^{x}&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
0.229 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{y}+y x \\
y \left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.366 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (4 x^{2}-\frac {1}{9}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{9}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.297 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+4 \left (x^{4}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.135 |
|
| \begin{align*}
y^{\prime \prime }+\frac {5 y^{\prime }}{x}+y&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y^{\prime \prime }+\frac {3 y^{\prime }}{x}+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \begin{align*}
x y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
x y^{\prime \prime }+\frac {y^{\prime }}{2}+\frac {y}{4}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.275 |
|
| \begin{align*}
x^{\prime }&=3-2 y \\
y^{\prime }&=2 x-2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.745 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
x^{\prime }+3 x+y&=0 \\
y^{\prime }+y-x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
x^{\prime }&=3 x-\frac {y}{2}-3 t^{2}-\frac {t}{2}+\frac {3}{2} \\
y^{\prime }&=2 y-2 t -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
x^{\prime }&=-7 x+y \\
y^{\prime }&=-2 x-5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
x^{\prime }&=2 x-9 y \\
y^{\prime }&=x+8 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=x+z \\
z^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
x^{\prime }&=y+z \\
y^{\prime }&=3 x+z \\
z^{\prime }&=3 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.774 |
|
| \begin{align*}
x^{\prime }&=8 y \\
y^{\prime }&=-2 z \\
z^{\prime }&=2 x+8 y-2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
x^{\prime }&=2 x+y-2 z+2-t \\
y^{\prime }&=1-x \\
z^{\prime }&=x+y-z+1-t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.511 |
|
| \begin{align*}
x^{\prime }&=-x+y+z+{\mathrm e}^{t} \\
y^{\prime }&=x-y+z+{\mathrm e}^{3 t} \\
z^{\prime }&=x+y+z+4 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| \begin{align*}
x^{\prime }&=x \cos \left (t \right ) \\
2 y^{\prime }&=\left ({\mathrm e}^{t}+{\mathrm e}^{-t}\right ) y \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{t}-y-5 x \\
y^{\prime }&={\mathrm e}^{2 t}+x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= {\frac {119}{900}} \\
y \left (0\right ) &= {\frac {211}{900}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \begin{align*}
x^{\prime }&=3 x+8 y \\
y^{\prime }&=-x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 6 \\
y \left (0\right ) &= -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.472 |
|
| \begin{align*}
x^{\prime }&=y \\
y^{\prime }&=-x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
x^{\prime }&=-4 x-4 y \\
x^{\prime }+4 y^{\prime }&=-4 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 1 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| \begin{align*}
x^{\prime }&=4 x-5 y \\
y^{\prime }&=x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
x^{\prime }&=x+y+t \\
y^{\prime }&=x-2 y+2 t \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -{\frac {7}{9}} \\
y \left (0\right ) &= -{\frac {5}{9}} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.418 |
|
| \begin{align*}
x^{\prime }&=x+5 y \\
y^{\prime }&=-x-3 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.573 |
|
| \begin{align*}
x^{\prime }+2 y^{\prime }&=17 x+8 y \\
13 x^{\prime }&=53 x+2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= -1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \begin{align*}
x^{\prime }&=y \\
x^{\prime }-y^{\prime }&=x+y \\
\end{align*}
With initial conditions \begin{align*}
x \left (\pi \right ) &= -1 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
x^{\prime }+y^{\prime }&={\mathrm e}^{-t}-y \\
2 x^{\prime }+y^{\prime }&=\sin \left (t \right )-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= -2 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
2 x^{\prime }&=6 x-y-6 t^{2}-t +3 \\
y^{\prime }&=2 y-2 t -1 \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 2 \\
y \left (0\right ) &= 3 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.656 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{y} \\
y^{\prime }&=\frac {1}{x} \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.031 |
|
| \begin{align*}
x^{\prime } t&=t -2 x \\
t y^{\prime }&=x t +y t +2 x-t \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.037 |
|
| \begin{align*}
x^{\prime }&=t +x \\
x \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.512 |
|
| \begin{align*}
x^{\prime }&=2 t \left (t +x\right ) \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.000 |
|
| \begin{align*}
x^{\prime }&=-x+t^{2} \\
x \left (1\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.790 |
|
| \begin{align*}
x^{\prime }&=t +2 \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
x^{\prime }&=x-13 y \\
y^{\prime }&=\frac {x}{4}-2 y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
x^{\prime }&=-x-3 y \\
y^{\prime }&=x-y \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
x^{\prime }&=3 x+y \\
y^{\prime }&=-2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.534 |
|
| \begin{align*}
x^{\prime }&=-x+2 y \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \begin{align*}
x^{\prime }&=-x+3 y \\
y^{\prime }&=-x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.580 |
|
| \begin{align*}
x^{\prime }&=-2 x-y \\
y^{\prime }&=3 x-y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| \begin{align*}
x^{\prime }&=3 x+7 y \\
y^{\prime }&=2 x+5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
x^{\prime }&=-2 x+\frac {5 y}{7} \\
y^{\prime }&=7 x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
x^{\prime }&=3 x-y \\
y^{\prime }&=x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \begin{align*}
x^{\prime }&=-x-y \\
y^{\prime }&=x-3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \begin{align*}
x^{\prime }&=-3 x+\alpha y \\
y^{\prime }&=2 x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \begin{align*}
x^{\prime }&=x+2 y-\sin \left (y\right )^{2} \\
y^{\prime }&=-x-3 y+x \left ({\mathrm e}^{\frac {x^{2}}{2}}-1\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.051 |
|
| \begin{align*}
x^{\prime }&=-x+3 y+x^{2} \sin \left (y\right ) \\
y^{\prime }&=-x-4 y+1-\cos \left (y^{2}\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.040 |
|
| \begin{align*}
x^{\prime }&=-2 x+8 \sin \left (y\right )^{2} \\
y^{\prime }&=x-3 y+4 x^{3} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.038 |
|
| \begin{align*}
x^{\prime }&=3 x-22 \sin \left (y\right )+x^{2}-y^{3} \\
y^{\prime }&=\sin \left (x\right )-5 y+{\mathrm e}^{x^{2}}-1 \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.037 |
|
| \begin{align*}
x^{\prime }&=-10 x+4 \,{\mathrm e}^{y}-4 \cos \left (y^{2}\right ) \\
y^{\prime }&=2 \,{\mathrm e}^{x}-2-y+x^{4} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.045 |
|
| \begin{align*}
x^{\prime }&=7 x+2 \sin \left (y\right )-4 y^{4} \\
y^{\prime }&={\mathrm e}^{x}-3 y-1+\frac {5 x^{2}}{2} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.040 |
|
| \begin{align*}
x^{\prime }&=-\frac {2 x}{3}+\frac {\sin \left (2 y\right )}{2}-x^{3} y \\
y^{\prime }&=-y-2 x+x^{4}-y^{7} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.042 |
|
| \begin{align*}
x^{\prime }&=\frac {5 x \,{\mathrm e}^{x}}{2}-3 y+\sin \left (x^{2}\right ) \\
y^{\prime }&=2 x+y \,{\mathrm e}^{-\frac {y^{2}}{2}}-y^{4} \cos \left (x\right ) \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.054 |
|
| \begin{align*}
x^{\prime }&=\frac {3 \sin \left (x\right )}{4}-7 y \left (1-y\right )^{{1}/{3}}+x^{3} \\
y^{\prime }&=\frac {2 x}{3}-3 y \cos \left (y\right )-11 y^{5} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.043 |
|
| \begin{align*}
x^{\prime }&=\frac {{\mathrm e}^{x}}{4}-\frac {1}{4}-9 y+x^{4} \\
y^{\prime }&=\frac {x}{5}-\sin \left (y\right )+y^{14} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.039 |
|
| \begin{align*}
x^{\prime }&=5 x+y \cos \left (y\right )-\frac {x^{3}}{3} \\
y^{\prime }&=3 x+2 y+\frac {x^{4}}{12}-y^{3} {\mathrm e}^{y} \\
\end{align*} |
system_of_ODEs |
✗ |
✗ |
✗ |
✗ |
0.058 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+7 y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.063 |
|
| \begin{align*}
y^{\prime \prime \prime }+5 y^{\prime \prime }+9 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+17 y^{\prime \prime }+17 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+12 y^{\prime }-10 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+18 y^{\prime \prime }+34 y^{\prime }+20 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+19 y^{\prime \prime }+23 y^{\prime }+10 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+11 y^{\prime \prime \prime }+41 y^{\prime \prime }+61 y^{\prime }+30 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.042 |
|
| \begin{align*}
y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }-15 y^{\prime \prime }+4 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
y^{\left (5\right )}+7 y^{\prime \prime \prime \prime }+33 y^{\prime \prime \prime }+88 y^{\prime \prime }+122 y^{\prime }+60 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+\alpha y^{\prime }+3 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.130 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+\alpha y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+3 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.051 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+\alpha y^{\prime \prime }+y^{\prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
y^{\prime \prime \prime }+\alpha y^{\prime \prime }+\beta y^{\prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.127 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+\alpha y^{\prime \prime }+2 y^{\prime }+\beta y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.042 |
|
| \begin{align*}
2 y^{\prime \prime \prime }+7 y^{\prime \prime }+7 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.051 |
|
| \begin{align*}
2 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }+28 y^{\prime \prime }+23 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| \begin{align*}
3 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }+19 y^{\prime \prime }+11 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
2 y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }+6 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.062 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+16 y^{\prime \prime }+24 y^{\prime }+20 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.053 |
|
| \begin{align*}
y^{\left (5\right )}+13 y^{\prime \prime \prime \prime }+43 y^{\prime \prime \prime }+51 y^{\prime \prime }+40 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.083 |
|