| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.080 |
|
| \begin{align*}
2 x^{3} y^{2}-y+\left (2 x^{2} y^{3}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
5.002 |
|
| \begin{align*}
y-1-y x +y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.930 |
|
| \begin{align*}
-y+y^{\prime } x&=x \tan \left (\frac {y}{x}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.459 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&={\mathrm e}^{y x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.102 |
|
| \begin{align*}
y y^{\prime \prime }-y y^{\prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
3.114 |
|
| \begin{align*}
2 y-x \left (\ln \left (x^{2} y\right )-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
20.745 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y x +x^{3} y^{3}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
7.931 |
|
| \begin{align*}
y^{\prime }&=\frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
9.106 |
|
| \begin{align*}
{\mathrm e}^{x}+3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.410 |
|
| \begin{align*}
y x +2 x^{3} y+x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.342 |
|
| \begin{align*}
4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.079 |
|
| \begin{align*}
y^{\prime \prime \prime }&=2 \left (y^{\prime \prime }-1\right ) \cot \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.794 |
|
| \begin{align*}
y+3 y^{2} x^{4}+\left (x +2 x^{2} y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.848 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {x^{2}-y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
60.994 |
|
| \begin{align*}
2 y \left (x \,{\mathrm e}^{x^{2}}+\sin \left (x \right ) \cos \left (x \right ) y\right )+\left (2 \,{\mathrm e}^{x^{2}}+3 y \sin \left (x \right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
0.992 |
|
| \begin{align*}
\cos \left (y\right )+\sin \left (y\right ) \left (x -\sin \left (y\right ) \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
23.713 |
|
| \begin{align*}
y^{3}+\left (3 x^{2}-2 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
15.256 |
|
| \begin{align*}
\left (1+y^{\prime }\right ) \ln \left (\frac {x +y}{x +3}\right )&=\frac {x +y}{x +3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.730 |
|
| \begin{align*}
2 y y^{\prime } x^{3}+3 y^{2} x^{2}+7&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.241 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
25.522 |
|
| \begin{align*}
x^{2} \left (-y+y^{\prime } x \right )&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.315 |
|
| \begin{align*}
y^{4}+y x +\left (x y^{3}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
13.891 |
|
| \begin{align*}
x^{2}+3 \ln \left (y\right )-\frac {x y^{\prime }}{y}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
10.969 |
|
| \begin{align*}
y^{\prime \prime } x&=x +y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.773 |
|
| \begin{align*}
y+\left (y x -x -y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
8.456 |
|
| \begin{align*}
y+2 y^{3} y^{\prime }&=\left (x +4 \ln \left (y\right ) y\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.132 |
|
| \begin{align*}
y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.228 |
|
| \begin{align*}
2 x^{{3}/{2}}+x^{2}+y^{2}+2 y \sqrt {x}\, y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.193 |
|
| \begin{align*}
2 x +y \cos \left (y x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.059 |
|
| \begin{align*}
y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.932 |
|
| \begin{align*}
2 y^{\prime }+x&=4 \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✓ |
✗ |
18.190 |
|
| \begin{align*}
2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.770 |
|
| \begin{align*}
y^{\prime }-6 x \,{\mathrm e}^{x -y}-1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.415 |
|
| \begin{align*}
\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
13.744 |
|
| \begin{align*}
\sin \left (x \right ) y+\cos \left (x \right )^{2}-\cos \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.907 |
|
| \begin{align*}
y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.936 |
|
| \begin{align*}
y^{\prime } \left (x -\ln \left (y^{\prime }\right )\right )&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.125 |
|
| \begin{align*}
\left (\cos \left (x \right )+1\right ) y^{\prime }+\sin \left (x \right ) \left (\sin \left (x \right )+\cos \left (x \right ) \sin \left (x \right )-y\right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.398 |
|
| \begin{align*}
x +\sin \left (\frac {y}{x}\right )^{2} \left (-y^{\prime } x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.373 |
|
| \begin{align*}
2 x y^{4} {\mathrm e}^{y}+2 x y^{3}+y+\left (x^{2} y^{4} {\mathrm e}^{y}-y^{2} x^{2}-3 x \right ) y^{\prime }&=0 \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✓ |
✓ |
✓ |
✗ |
6.615 |
|
| \begin{align*}
x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.574 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+9 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.111 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.107 |
|
| \begin{align*}
y^{\prime \prime \prime }+8 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.074 |
|
| \begin{align*}
y^{\prime \prime \prime }-8 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.072 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.088 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.123 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.133 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+5 y^{\prime \prime }+5 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.122 |
|
| \begin{align*}
y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
y^{\left (6\right )}-64 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.120 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+10 y&=3 x \,{\mathrm e}^{-3 x}-2 \,{\mathrm e}^{3 x} \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.564 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.039 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=\left (x +{\mathrm e}^{x}\right ) \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.618 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=\sinh \left (x \right ) \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.430 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\cosh \left (x \right ) \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.868 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right )+\cos \left (x \right ) x \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y&={\mathrm e}^{2 x} \sin \left (2 x \right )+2 x^{2} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.538 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime }&=x^{2}+x \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.267 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime }&=7 x -3 \cos \left (x \right ) \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=\sin \left (x \right ) \cos \left (2 x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.021 |
|
| \begin{align*}
y^{\left (5\right )}-3 y^{\prime \prime \prime }+y&=9 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&=48 x \,{\mathrm e}^{x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.253 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime }&=9 x^{2} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.229 |
|
| \begin{align*}
y^{\left (5\right )}+4 y^{\prime \prime \prime }&=7+x \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.264 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=36 x \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.694 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+16 y&=64 \cos \left (2 x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }-y&=44 \sin \left (3 x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }+5 y^{\prime }+5 y&=5 \cos \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.255 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+5 y&=5 \sin \left (2 x \right ) {\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=4 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=8 \sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.813 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.596 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime }&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.237 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{x} \left (x +1\right )+2 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.406 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=4 \,{\mathrm e}^{x} \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=4 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.682 |
|
| \begin{align*}
y^{\prime \prime }-y&=12 \,{\mathrm e}^{x} x^{2}+3 \,{\mathrm e}^{2 x}+10 \cos \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.046 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \sin \left (x \right )-3 \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.295 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{x} \left (x^{2}+10\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.535 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=96 x^{2} {\mathrm e}^{2 x}+4 \,{\mathrm e}^{-2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.159 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=5 \cos \left (x \right )+10 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.960 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=4 x -2+2 \,{\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.528 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=4 x \,{\mathrm e}^{2 x} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.093 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=15 \sin \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.249 |
|
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y&=40 \sin \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.236 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=2 \,{\mathrm e}^{x}+5 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.386 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=10 \,{\mathrm e}^{x} \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime }-4 y&=50 \,{\mathrm e}^{2 x}+50 \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.465 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=12 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.397 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=32 \,{\mathrm e}^{2 x}+16 x^{3} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=72 \,{\mathrm e}^{3 x}+729 x^{2} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {1}{x}-\frac {2}{x^{3}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {1}{\sinh \left (x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{x}}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.766 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\sin \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.702 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+2 y&=\sin \left ({\mathrm e}^{-x}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.675 |
|