| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x&=t \left (1+x^{\prime }\right )+x^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.615 |
|
| \begin{align*}
x^{\prime }&=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 |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| \begin{align*}
x^{\prime }&=a y \\
y^{\prime }&=-a x \\
\end{align*}
With initial conditions \begin{align*}
x \left (0\right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.992 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.676 |
|
| \begin{align*}
x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
59.761 |
|
| \begin{align*}
x^{\prime \prime }+\frac {x^{\prime }}{t}+q \left (t \right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
44.109 |
|
| \begin{align*}
2 x^{\prime \prime }+x^{\prime }-x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
x^{\prime \prime }+8 x^{\prime }+16 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }-15 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.525 |
|
| \begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.535 |
|
| \begin{align*}
4 x^{\prime }+2 x^{\prime \prime }&=-5 x \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.712 |
|
| \begin{align*}
x^{\prime \prime }-6 x^{\prime }+9 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }-\beta x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+k x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
x^{\prime \prime }+b x^{\prime }+c x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \begin{align*}
x^{\prime \prime }+5 x^{\prime }+6 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
x^{\prime \prime }+p x^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.487 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }-2 x&=0 \\
x \left (0\right ) &= a \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
x^{\prime \prime }-2 a x^{\prime }+b x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \begin{align*}
x^{\prime \prime }+\lambda ^{2} x&=0 \\
x \left (0\right ) &= 0 \\
x \left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.669 |
|
| \begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.644 |
|
| \begin{align*}
x^{\prime \prime }-x&=0 \\
x \left (0\right ) &= 0 \\
x \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.132 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }-2 x&=0 \\
x \left (0\right ) &= 0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.717 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+5 x&=0 \\
x \left (0\right ) &= 0 \\
x \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+5 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (\theta \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (\infty \right ) &= a \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✗ |
✓ |
18.523 |
|
| \begin{align*}
x^{\prime \prime }-4 x&=t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.567 |
|
| \begin{align*}
x^{\prime \prime }-4 x&=4 t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.548 |
|
| \begin{align*}
x^{\prime \prime }+x&=t^{2}-2 t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.630 |
|
| \begin{align*}
x^{\prime \prime }+x&=3 t^{2}+t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{-3 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \begin{align*}
x^{\prime \prime }-x&=3 \,{\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{2 t} t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
x^{\prime \prime }-3 x^{\prime }-x&=t^{2}+t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+13 x&=20 \,{\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }-2 x&=2 t +{\mathrm e}^{t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\cos \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| \begin{align*}
x^{\prime \prime }+x&=\sin \left (2 t \right )-\cos \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=\cos \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.657 |
|
| \begin{align*}
x^{\prime \prime }+x&=t \sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.913 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }&=t \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.260 |
|
| \begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{k t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }-2 x&=3 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.566 |
|
| \begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=3 \,{\mathrm e}^{t} t \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+3 x&=2 \,{\mathrm e}^{t}-5 \,{\mathrm e}^{2 t} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.749 |
|
| \begin{align*}
x^{\prime \prime }+2 x&=\cos \left (\sqrt {2}\, t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\sin \left (2 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
x^{\prime \prime }+x&=2 \sin \left (t \right )+2 \cos \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| \begin{align*}
x^{\prime \prime }+9 x&=\sin \left (t \right )+\sin \left (3 t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.217 |
|
| \begin{align*}
x^{\prime \prime }-x&=t \\
x \left (0\right ) &= 0 \\
x \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.662 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+x&=k \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.747 |
|
| \begin{align*}
x^{\prime \prime }-2 x&=2 \,{\mathrm e}^{t} \\
x \left (0\right ) &= 0 \\
x \left (a \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \begin{align*}
x^{\prime \prime }+\frac {\left (t^{5}+1\right ) x}{t^{4}+5}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
15.306 |
|
| \begin{align*}
x^{\prime \prime }+\sqrt {t^{6}+3 t^{5}+1}\, x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✗ |
✗ |
✗ |
✗ |
7.269 |
|
| \begin{align*}
x^{\prime \prime }+2 t^{3} x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.363 |
|
| \begin{align*}
x^{\prime \prime }-p \left (t \right ) x&=q \left (t \right ) \\
x \left (a \right ) &= 0 \\
x \left (b \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
10.412 |
|
| \begin{align*}
x^{\prime \prime }+p \left (t \right ) x^{\prime }+q \left (t \right ) x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
30.873 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.536 |
|
| \begin{align*}
x^{\prime \prime }-\frac {x^{\prime } t}{4}+x&=0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✗ |
1.125 |
|
| \begin{align*}
x^{\prime \prime }-\frac {x^{\prime }}{t}&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime } \left (x-1\right )&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
✗ |
0.720 |
|
| \begin{align*}
x^{\prime \prime }&=2 {x^{\prime }}^{3} x \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.609 |
|
| \begin{align*}
x x^{\prime \prime }-2 {x^{\prime }}^{2}-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
14.452 |
|
| \begin{align*}
x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2}&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.850 |
|
| \begin{align*}
x x^{\prime \prime }-{x^{\prime }}^{2}+{\mathrm e}^{t} x^{2}&=0 \\
x \left (0\right ) &= -1 \\
x^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.540 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-2 x&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.894 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+a t x^{\prime }+x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.855 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-x^{\prime } t -3 x&=0 \\
x \left (1\right ) &= 0 \\
x^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.026 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+x^{\prime } t +x&=t \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.960 |
|
| \begin{align*}
t^{2} x^{\prime \prime }+3 x^{\prime } t -3 x&=t^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.123 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime } t +3 x&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
1.191 |
|
| \begin{align*}
2 x^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.075 |
|
| \begin{align*}
x^{\prime \prime \prime }-x^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.072 |
|
| \begin{align*}
x^{\prime \prime \prime }+5 x^{\prime \prime }-6 x&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.085 |
|
| \begin{align*}
x^{\prime \prime \prime }-4 x^{\prime \prime }+x^{\prime }-4 x&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.092 |
|
| \begin{align*}
x^{\prime \prime \prime }-3 x^{\prime \prime }+4 x&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.097 |
|
| \begin{align*}
x^{\prime \prime \prime }+4 x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -1 \\
x^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
x^{\prime \prime \prime }-x^{\prime }&=0 \\
x \left (0\right ) &= 1 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✗ |
✓ |
✓ |
✓ |
1.766 |
|
| \begin{align*}
x^{\prime \prime \prime }-x^{\prime }&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.142 |
|
| \begin{align*}
x^{\prime \prime \prime }+x^{\prime \prime }-2 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✗ |
✓ |
✗ |
✗ |
10.998 |
|
| \begin{align*}
x^{\prime \prime \prime }-3 x^{\prime }+k x&=0 \\
x \left (0\right ) &= 1 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✗ |
✓ |
✗ |
✗ |
8.073 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-6 x^{\prime \prime }+5 x&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.096 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
x^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-x^{\prime \prime }&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-4 x^{\prime \prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x \left (\infty \right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✗ |
✓ |
✓ |
✓ |
0.886 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }-8 x^{\prime \prime \prime }+23 x^{\prime \prime }-28 x^{\prime }+12 x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✗ |
✓ |
✓ |
✓ |
0.443 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+2 x^{\prime \prime }-4 x&=0 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.274 |
|
| \begin{align*}
x^{\left (5\right )}-x^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.097 |
|
| \begin{align*}
x^{\left (5\right )}+x^{\prime \prime \prime \prime }-x^{\prime }-x&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
x^{\left (5\right )}+x&=0 \\
x \left (\infty \right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
8.886 |
|
| \begin{align*}
x^{\left (6\right )}-x^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
x^{\left (6\right )}-64 x&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.125 |
|
| \begin{align*}
x^{\prime \prime \prime \prime }+3 x^{\prime \prime \prime }+2 x^{\prime \prime }&={\mathrm e}^{t} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
x^{\prime \prime \prime }+4 x^{\prime }&=\sec \left (2 t \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.905 |
|
| \begin{align*}
x^{\prime \prime \prime }-x^{\prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \begin{align*}
x^{\prime \prime \prime }-x^{\prime }&=t \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
x^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.214 |
|