| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.386 |
|
| \begin{align*}
u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.801 |
|
| \begin{align*}
u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.501 |
|
| \begin{align*}
u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.237 |
|
| \begin{align*}
u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.479 |
|
| \begin{align*}
y^{\prime \prime }-a^{2} y&=\frac {6 y}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.252 |
|
| \begin{align*}
y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.338 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.548 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {25}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.294 |
|
| \begin{align*}
y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.263 |
|
| \begin{align*}
y^{\prime \prime }+y \,{\mathrm e}^{2 x}&=n^{2} y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.210 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y}{4 x}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.406 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.729 |
|
| \begin{align*}
y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| \begin{align*}
y^{\prime } x&=y \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.353 |
|
| \begin{align*}
x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }&=0 \\
y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
11.325 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }&=y \ln \left (y\right ) \\
y \left (\frac {\pi }{3}\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.604 |
|
| \begin{align*}
y y^{\prime } x +1+y^{2}&=0 \\
y \left (5\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.471 |
|
| \begin{align*}
y y^{\prime } x -y x&=y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y^{2}+x}{x^{2} y-y} \\
y \left (\sqrt {2}\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.716 |
|
| \begin{align*}
y y^{\prime }+x y^{2}-8 x&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.169 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.363 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime }&=y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.930 |
|
| \begin{align*}
y^{\prime }-y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.101 |
|
| \begin{align*}
2 y^{\prime }&=3 \left (-2+y\right )^{{1}/{3}} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.985 |
|
| \begin{align*}
\left (y x +x \right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.536 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \begin{align*}
x^{2} y^{\prime }+3 y x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.193 |
|
| \begin{align*}
y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.216 |
|
| \begin{align*}
2 y^{\prime } x +y&=2 x^{{5}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.189 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y&=\cos \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sqrt {x^{2}+1}}&=\frac {1}{x +\sqrt {x^{2}+1}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.204 |
|
| \begin{align*}
\left ({\mathrm e}^{x}+1\right ) y^{\prime }+2 \,{\mathrm e}^{x} y&=\left ({\mathrm e}^{x}+1\right ) {\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }+y&=\ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=y x +2 x \sqrt {-x^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.228 |
|
| \begin{align*}
y^{\prime }+y \tanh \left (x \right )&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.232 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
x^{\prime }&=\cos \left (y \right )-x \tan \left (y \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
x^{\prime }+x-{\mathrm e}^{y}&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.178 |
|
| \begin{align*}
x^{\prime }&=\frac {3 y^{{2}/{3}}-x}{3 y} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y^{\prime }+y&=x y^{{2}/{3}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.367 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=2 x^{{3}/{2}} \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.321 |
|
| \begin{align*}
3 y^{2} y^{\prime } x +3 y^{3}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.880 |
|
| \begin{align*}
2 x \,{\mathrm e}^{3 y}+{\mathrm e}^{x}+\left (3 x^{2} {\mathrm e}^{3 y}-y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
5.517 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }+x +y+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.519 |
|
| \begin{align*}
\cos \left (x \right ) \cos \left (y\right )+\sin \left (x \right )^{2}-\left (\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
unknown |
✓ |
✓ |
✓ |
✗ |
33.688 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.691 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.338 |
|
| \begin{align*}
y x +\left (y^{2}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.337 |
|
| \begin{align*}
y^{2}-y x +\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
25.205 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.954 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.206 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.034 |
|
| \begin{align*}
y^{\prime }&=x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
10.205 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{2}}{x}+\frac {y}{x}-2 x \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.475 |
|
| \begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-x}+y-{\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.497 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
y^{\prime \prime }+9 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.701 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.827 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.682 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.328 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.222 |
|
| \begin{align*}
y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-6 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.091 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.142 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.073 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=10 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.524 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=16 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.514 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.426 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=24 \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.438 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=12 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.511 |
|
| \begin{align*}
y^{\prime \prime }-16 y&=40 \,{\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.535 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.560 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=6 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.594 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=100 \cos \left (4 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+12 y&=80 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.622 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+25 y&=120 \sin \left (5 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
5 y^{\prime \prime }+12 y^{\prime }+20 y&=120 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.577 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=30 \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=16 \cos \left (4 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+17 y&=60 \,{\mathrm e}^{-4 x} \sin \left (5 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.571 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+5 y&=40 \,{\mathrm e}^{-\frac {3 x}{2}} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.588 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+8 y&=30 \,{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {5 x}{2}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
5 y^{\prime \prime }+6 y^{\prime }+2 y&=x^{2}+6 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }&=2 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=12 x \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=16 x^{2} {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \begin{align*}
y^{\prime \prime }+y&=8 x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.788 |
|