| # |
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]] |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| \begin{align*}
-4 y^{\prime }+y^{\prime \prime \prime }&=30 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.169 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=x^{3} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.367 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=\tan \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-81 y&=\sinh \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.602 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y&=12 x \sin \left (x^{2}\right ) \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
y^{\prime \prime }+36 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.611 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+36 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.264 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.702 |
|
| \begin{align*}
y^{\prime \prime }-36 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.824 |
|
| \begin{align*}
y^{\prime \prime }-9 y^{\prime }+14 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.110 |
|
| \begin{align*}
16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.301 |
|
| \begin{align*}
y^{\prime }+2 y^{\prime \prime } x&=\sqrt {x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
9.164 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.079 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.974 |
|
| \begin{align*}
y^{\prime \prime }+3 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.418 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
7.830 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\frac {5 y}{2}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.944 |
|
| \begin{align*}
y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.083 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.720 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.253 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.871 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.288 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.359 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -30 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.398 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-30 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.515 |
|
| \begin{align*}
16 y^{\prime \prime }-8 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.784 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
30.879 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }&=8 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.153 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
15.986 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.776 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
2 y^{\prime \prime }-7 y^{\prime }+3&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.661 |
|
| \begin{align*}
y^{\prime \prime }+20 y^{\prime }+100 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.399 |
|
| \begin{align*}
y^{\prime \prime } x&=3 y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
32.752 |
|
| \begin{align*}
y^{\prime \prime }-5 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.019 |
|
| \begin{align*}
y^{\prime \prime }-9 y^{\prime }+14 y&=98 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
35.351 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+36 y&=25 \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
34.773 |
|
| \begin{align*}
y^{\prime \prime }-9 y^{\prime }+14 y&=576 x^{2} {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
40.420 |
|
| \begin{align*}
y^{\prime \prime }-12 y^{\prime }+36 y&=81 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
22.149 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=3 \sqrt {x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.498 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
36.247 |
|
| \begin{align*}
y^{\prime \prime }+36 y&=6 \sec \left (6 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
7.293 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=18 \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.334 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=10 \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
26.771 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x -2 y&=10 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.916 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=2 \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
11.703 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=-3 x {y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
15.687 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.003 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=\frac {1}{x^{2}+1} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
21.435 |
|
| \begin{align*}
4 y^{\prime \prime }-12 y^{\prime }+9 y&=x \,{\mathrm e}^{\frac {3 x}{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
25.893 |
|
| \begin{align*}
3 y^{\prime \prime }+8 y^{\prime }-3 y&=123 x \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
42.509 |
|
| \begin{align*}
y^{\prime \prime \prime }+8 y&={\mathrm e}^{-2 x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.156 |
|
| \begin{align*}
y^{\left (6\right )}-64 y&={\mathrm e}^{-2 x} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (x +1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
9.035 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
17.729 |
|
| \begin{align*}
y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.285 |
|
| \begin{align*}
-2 y+y^{\prime }&=t^{3} \\
y \left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.454 |
|
| \begin{align*}
3 y+y^{\prime }&=\operatorname {Heaviside}\left (t -4\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.153 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.456 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=3 \operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.636 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.540 |
|
| \begin{align*}
t y^{\prime \prime }+y^{\prime }+t y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
0.396 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.267 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.343 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.357 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.229 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.333 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \begin{align*}
y^{\prime }&=\operatorname {Heaviside}\left (t -3\right ) \\
y \left (0\right ) &= 4 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
y^{\prime \prime }&=\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.285 |
|
| \begin{align*}
y^{\prime \prime }&=\operatorname {Heaviside}\left (-2+t \right ) \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.292 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.557 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.272 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
4.087 |
|