| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=12 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.595 |
|
| \begin{align*}
-4 y^{\prime }+y^{\prime \prime \prime }&=30 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.148 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=x^{3} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\tan \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.053 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-81 y&=\sinh \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 x y^{\prime }+9 y&=12 x \sin \left (x^{2}\right ) \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
y^{\prime \prime }+36 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+36 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.516 |
|
| \begin{align*}
y^{\prime \prime }-36 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.996 |
|
| \begin{align*}
y^{\prime \prime }-9 y^{\prime }+14 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
16 y-7 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.437 |
|
| \begin{align*}
y^{\prime }+2 x y^{\prime \prime }&=\sqrt {x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.128 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.073 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.360 |
|
| \begin{align*}
y^{\prime \prime }+3 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.737 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 x y^{\prime }+9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.488 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\frac {5 y}{2}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.425 |
|
| \begin{align*}
y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.082 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.773 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.630 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.347 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-30 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.974 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-30 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.388 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 x y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }&=8 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.053 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.565 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| \begin{align*}
2 y^{\prime \prime }-7 y^{\prime }+3&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.346 |
|
| \begin{align*}
y^{\prime \prime }+20 y^{\prime }+100 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
x y^{\prime \prime }&=3 y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.940 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.382 |
|
| \begin{align*}
y^{\prime \prime }-9 y^{\prime }+14 y&=98 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+36 y&=25 \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.653 |
|
| \begin{align*}
y^{\prime \prime }-9 y^{\prime }+14 y&=576 x^{2} {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.505 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+36 y&=81 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.567 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-9 y&=3 \sqrt {x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.660 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+36 y&=3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \begin{align*}
y^{\prime \prime }+36 y&=6 \sec \left (6 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=18 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.477 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=10 \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-x y^{\prime }-2 y&=10 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.608 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=2 \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
-y^{\prime }+x y^{\prime \prime }&=-3 x {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.968 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y&=6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.807 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=\frac {1}{x^{2}+1} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.474 |
|
| \begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+9 y&=x \,{\mathrm e}^{\frac {3 x}{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.612 |
|
| \begin{align*}
3 y^{\prime \prime }+8 y^{\prime }-3 y&=123 x \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \begin{align*}
y^{\prime \prime \prime }+8 y&={\mathrm e}^{-2 x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.141 |
|
| \begin{align*}
y^{\left (6\right )}-64 y&={\mathrm e}^{-2 x} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.189 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{\left (x +1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.812 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.613 |
|
| \begin{align*}
y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| \begin{align*}
-2 y+y^{\prime }&=t^{3} \\
y \left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
3 y+y^{\prime }&=\operatorname {Heaviside}\left (-4+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=t^{3} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=20 \,{\mathrm e}^{4 t} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.144 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }+6 y&={\mathrm e}^{4 t} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=t^{2} {\mathrm e}^{4 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }+6 y&=7 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+13 y&=4 t +2 \,{\mathrm e}^{2 t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
y^{\prime \prime \prime }-27 y&={\mathrm e}^{-3 t} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.464 |
|
| \begin{align*}
t y^{\prime \prime }+y^{\prime }+y t&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 9 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=27 t^{3} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+7 y&=165 \,{\mathrm e}^{4 t} \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+17 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.244 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=t^{2} {\mathrm e}^{3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.208 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.262 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+17 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -12 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.238 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{t} \sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.313 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+40 y&=122 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=24 \,{\mathrm e}^{-3 t} \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.288 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&={\mathrm e}^{2 t} \sin \left (3 t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.332 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \begin{align*}
y^{\prime \prime }+4 y&={\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]] |
✓ |
✓ |
✓ |
✓ |
0.306 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (2 t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.312 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sin \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=1 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\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]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\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]] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{t} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (-3+t \right ) \\
y \left (0\right ) &= 4 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \begin{align*}
y^{\prime \prime }&=\operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.236 |
|
| \begin{align*}
y^{\prime \prime }&=\operatorname {Heaviside}\left (t -2\right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.231 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\operatorname {Heaviside}\left (t -10\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.059 |
|
| \begin{align*}
y^{\prime }&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.627 |
|
| \begin{align*}
y^{\prime \prime }&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.244 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\left \{\begin {array}{cc} 0 & t <1 \\ 1 & 1<t <3 \\ 0 & 3<t \end {array}\right . \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.921 |
|