| # |
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]] |
✓ |
✓ |
✓ |
✓ |
0.562 |
|
| \begin{align*}
u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.501 |
|
| \begin{align*}
u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
y^{\prime \prime }-a^{2} y&=\frac {6 y}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
y^{\prime \prime }+n^{2} y&=\frac {6 y}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.598 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.383 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
y^{\prime \prime }+q y^{\prime }&=\frac {2 y}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.502 |
|
| \begin{align*}
y^{\prime \prime }+y \,{\mathrm e}^{2 x}&=n^{2} y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.128 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y}{4 x}&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.188 |
|
| \begin{align*}
y^{\prime \prime } x +3 y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.634 |
|
| \begin{align*}
y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
y^{\prime } x&=y \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.977 |
|
| \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] | ✓ | ✓ | ✓ | ✗ | 5.645 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }&=y \ln \left (y\right ) \\
y \left (\frac {\pi }{3}\right ) &= {\mathrm e} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| \begin{align*}
x y^{\prime } y+1+y^{2}&=0 \\
y \left (5\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.123 |
|
| \begin{align*}
x y^{\prime } y-y x&=y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.169 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y^{2}+x}{x^{2} y-y} \\
y \left (\sqrt {2}\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.629 |
|
| \begin{align*}
y^{\prime } y+x y^{2}-8 x&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.348 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.457 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime }&=y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.994 |
|
| \begin{align*}
y^{\prime }-y x&=x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.721 |
|
| \begin{align*}
2 y^{\prime }&=3 \left (y-2\right )^{{1}/{3}} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.884 |
|
| \begin{align*}
\left (y x +x \right ) y^{\prime }+y&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.144 |
|
| \begin{align*}
y^{\prime }+y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.081 |
|
| \begin{align*}
x^{2} y^{\prime }+3 y x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.069 |
|
| \begin{align*}
y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
2 y^{\prime } x +y&=2 x^{{5}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.070 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y&=\cos \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sqrt {x^{2}+1}}&=\frac {1}{x +\sqrt {x^{2}+1}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
0.085 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
0.125 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }+y&=\ln \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.127 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=y x +2 x \sqrt {-x^{2}+1} \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 0.093 |
|
| \begin{align*}
y^{\prime }+y \tanh \left (x \right )&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.122 |
|
| \begin{align*}
y^{\prime }+y \cos \left (x \right )&=\sin \left (2 x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.115 |
|
| \begin{align*}
x^{\prime }&=\cos \left (y \right )-x \tan \left (y \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.119 |
|
| \begin{align*}
x^{\prime }+x-{\mathrm e}^{y}&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.087 |
|
| \begin{align*}
x^{\prime }&=\frac {3 y^{{2}/{3}}-x}{3 y} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.071 |
|
| \begin{align*}
y^{\prime }+y&=x y^{{2}/{3}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.874 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=2 x^{{3}/{2}} \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.346 |
|
| \begin{align*}
3 y^{2} y^{\prime } x +3 y^{3}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.970 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
2.741 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }+x +y+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.174 |
|
| \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 |
✓ |
✓ |
✓ |
✗ |
31.997 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.976 |
|
| \begin{align*}
y^{\prime } y&=\sqrt {y^{2}+x^{2}}-x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.731 |
|
| \begin{align*}
y x +\left (y^{2}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.376 |
|
| \begin{align*}
y^{2}-y x +\left (x^{2}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
5.782 |
|
| \begin{align*}
y^{\prime }&=\cos \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.527 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.467 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.412 |
|
| \begin{align*}
y^{\prime }&=x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \\
\end{align*} | [[_homogeneous, ‘class G‘], _rational, _Riccati] | ✓ | ✓ | ✓ | ✓ | 3.880 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{2}}{x}+\frac {y}{x}-2 x \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.733 |
|
| \begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-x}+y-{\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.138 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.163 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
y^{\prime \prime }+9 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.204 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.501 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.240 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \begin{align*}
y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.170 |
|
| \begin{align*}
y^{\prime \prime }+\left (1+2 i\right ) y^{\prime }+\left (-1+i\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.154 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.042 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-6 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.043 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }-5 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.087 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }&=10 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.923 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=16 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.268 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=24 \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=12 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=3 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
y^{\prime \prime }-16 y&=40 \,{\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=6 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+10 y&=100 \cos \left (4 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+12 y&=80 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.453 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.387 |
|
| \begin{align*}
y^{\prime \prime }+8 y^{\prime }+25 y&=120 \sin \left (5 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
5 y^{\prime \prime }+12 y^{\prime }+20 y&=120 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=30 \sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=16 \cos \left (4 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \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]] | ✓ | ✓ | ✓ | ✓ | 0.418 |
|
| \begin{align*}
5 y^{\prime \prime }+6 y^{\prime }+2 y&=x^{2}+6 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
2 y^{\prime \prime }+y^{\prime }&=2 x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=12 x \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=16 x^{2} {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| \begin{align*}
y^{\prime \prime }+y&=8 x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|