| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (-x +3\right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.882 |
|
| \begin{align*}
2 y^{\prime \prime } x +\left (x +1\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.919 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.591 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
✗ |
✓ |
✗ |
0.218 |
|
| \begin{align*}
y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.275 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (4 x +4\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.696 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.757 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.763 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
3.480 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.733 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✓ |
0.949 |
|
| \begin{align*}
\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (5 x +1\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y&=0 \\
\end{align*} Series expansion around \(x=-1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.032 |
|
| \begin{align*}
\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (3 x +5\right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=3\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.988 |
|
| \begin{align*}
\left (1-x \right ) x y^{\prime \prime }+\left (1-3 x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.686 |
|
| \begin{align*}
n \left (n +1\right ) y-2 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
1.456 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (-n^{2}+x^{2}\right ) y&=0 \\
\end{align*} Series expansion around \(x=\infty \). |
[_Bessel] |
✗ |
✗ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
y^{\prime }+y&=3 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.186 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=2 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=3 x^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-x} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.279 |
|
| \begin{align*}
y^{\prime \prime } x +\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.331 |
|
| \begin{align*}
y^{\prime \prime } x +\left (3+2 x \right ) y^{\prime }+\left (x +3\right ) y&=3 \,{\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✗ |
✗ |
0.385 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y&=0 \\
y \left (0\right ) &= y_{0} \\
y^{\prime }\left (0\right ) &= \operatorname {yd}_{0} \\
\end{align*} Using Laplace transform method. |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
2.932 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.528 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&=4 \,{\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.341 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=t^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=f \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.536 |
|
| \begin{align*}
x^{\prime }&=x+3 y \\
y^{\prime }&=3 x+y \\
\end{align*} With initial conditions \begin{align*}
x \left (0\right ) &= 5 \\
y \left (0\right ) &= 1 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
x^{\prime }&=x+2 y \\
y^{\prime }&=3 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
x^{\prime }&=x+2 y+t -1 \\
y^{\prime }&=3 x+2 y-5 t -2 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
x^{\prime }&=x+y \\
y^{\prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.281 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.245 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
x^{\prime }&=5 x+4 y \\
y^{\prime }&=-x+y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.430 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.297 |
|
| \begin{align*}
x^{\prime }&=-4 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
x^{\prime }&=7 x+6 y \\
y^{\prime }&=2 x+6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \begin{align*}
x^{\prime }&=x-2 y \\
y^{\prime }&=4 x+5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.601 |
|
| \begin{align*}
x^{\prime }&=x+y-5 t +2 \\
y^{\prime }&=4 x-2 y-8 t -8 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
x^{\prime }&=2 x \\
y^{\prime }&=3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \begin{align*}
x^{\prime }&=-x-2 y \\
y^{\prime }&=4 x-5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \begin{align*}
x^{\prime }&=-3 x+4 y \\
y^{\prime }&=-2 x+3 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \begin{align*}
x^{\prime }&=5 x+2 y \\
y^{\prime }&=-17 x-5 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.490 |
|
| \begin{align*}
x^{\prime }&=-4 x-y \\
y^{\prime }&=x-2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| \begin{align*}
x^{\prime }&=4 x-3 y \\
y^{\prime }&=8 x-6 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
x^{\prime }&=4 x-2 y \\
y^{\prime }&=5 x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.531 |
|
| \begin{align*}
x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
198.194 |
|
| \begin{align*}
x^{\prime }&=3 t^{2}+4 t \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \begin{align*}
x^{\prime }&=b \,{\mathrm e}^{t} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{t^{2}+1} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.440 |
|
| \begin{align*}
x^{\prime }&=\frac {1}{\sqrt {t^{2}+1}} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
x^{\prime }&=\cos \left (t \right ) \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.469 |
|
| \begin{align*}
x^{\prime }&=\frac {\cos \left (t \right )}{\sin \left (t \right )} \\
x \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| \begin{align*}
x^{\prime }&=x^{2}-3 x+2 \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
6.204 |
|
| \begin{align*}
x^{\prime }&=b \,{\mathrm e}^{x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.150 |
|
| \begin{align*}
x^{\prime }&=\left (x-1\right )^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.944 |
|
| \begin{align*}
x^{\prime }&=\sqrt {x^{2}-1} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.209 |
|
| \begin{align*}
x^{\prime }&=2 \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.301 |
|
| \begin{align*}
x^{\prime }&=\tan \left (x\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.561 |
|
| \begin{align*}
3 t^{2} x-t x+\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
1+2 x+\left (-t^{2}+4\right ) x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.841 |
|
| \begin{align*}
x^{\prime }&=\cos \left (\frac {x}{t}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.681 |
|
| \begin{align*}
\left (t^{2}-x^{2}\right ) x^{\prime }&=t x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.401 |
|
| \begin{align*}
x^{\prime } {\mathrm e}^{3 t}+3 x \,{\mathrm e}^{3 t}&=2 t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.945 |
|
| \begin{align*}
2 t +3 x+\left (3 t -x\right ) x^{\prime }&=t^{2} \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
4.658 |
|
| \begin{align*}
x^{\prime }+2 x&={\mathrm e}^{t} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| \begin{align*}
x^{\prime }+x \tan \left (t \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.463 |
|
| \begin{align*}
x^{\prime }-x \tan \left (t \right )&=4 \sin \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| \begin{align*}
t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x&=t^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.974 |
|
| \begin{align*}
x^{\prime }+2 t x+t x^{4}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.846 |
|
| \begin{align*}
t x^{\prime }+x \ln \left (t \right )&=t^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.520 |
|
| \begin{align*}
t x^{\prime }+x g \left (t \right )&=h \left (t \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.573 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.369 |
|
| \begin{align*}
x^{\prime }&=-\lambda x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.758 |
|
| \begin{align*}
x^{\prime }&=x \\
y^{\prime }&=x+2 y \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \begin{align*}
x^{\prime \prime }-5 x^{\prime }+6 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.187 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+4 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \begin{align*}
x^{\prime \prime }-4 x^{\prime }+5 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| \begin{align*}
x^{\prime \prime }+3 x^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.294 |
|
| \begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.318 |
|
| \begin{align*}
x^{\prime \prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.467 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
x^{\prime \prime }-2 x^{\prime }+2 x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
x^{\prime \prime }-x&=t^{2} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
x^{\prime \prime }-x&={\mathrm e}^{t} \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.521 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+4 x&={\mathrm e}^{t} \cos \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.719 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }+x&=\sin \left (2 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.610 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&=t \sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.692 |
|