| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (x y^{2}+x^{3}\right ) y^{\prime }&=2 y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.305 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.139 |
|
| \begin{align*}
y^{\prime }+y \tanh \left (x \right )&=2 \sinh \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.871 |
|
| \begin{align*}
y^{\prime } x -2 y&=\cos \left (x \right ) x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.538 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.824 |
|
| \begin{align*}
y^{\prime } x +3 y&=y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.038 |
|
| \begin{align*}
x \left (y-3\right ) y^{\prime }&=4 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.233 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }&=x^{2} y \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.278 |
|
| \begin{align*}
x^{3}+\left (1+y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.842 |
|
| \begin{align*}
\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= \frac {\pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.319 |
|
| \begin{align*}
x^{2} \left (1+y\right )+y^{2} \left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.248 |
|
| \begin{align*}
\left (-x +2 y\right ) y^{\prime }&=2 x +y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
45.083 |
|
| \begin{align*}
y x +y^{2}+\left (x^{2}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
52.712 |
|
| \begin{align*}
x^{3}+y^{3}&=3 y^{\prime } y^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.647 |
|
| \begin{align*}
y-3 x +\left (3 x +4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.808 |
|
| \begin{align*}
\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=y^{3}+3 x^{2} y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
138.889 |
|
| \begin{align*}
-y+y^{\prime } x&=x^{3}+3 x^{2}-2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.289 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) y&=\sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
-y+y^{\prime } x&=\cos \left (x \right ) x^{3} \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+3 y x&=5 x \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=5 \,{\mathrm e}^{\cos \left (x \right )} \\
y \left (\frac {\pi }{2}\right ) &= -4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| \begin{align*}
\left (3 x +3 y-4\right ) y^{\prime }&=-x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
15.647 |
|
| \begin{align*}
x -x y^{2}&=\left (x +x^{2} y\right ) y^{\prime } \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
23.720 |
|
| \begin{align*}
x -y-1+\left (4 y+x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
31.434 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
106.891 |
|
| \begin{align*}
\left (y x +1\right ) y+x \left (1+y x +y^{2} x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
8.155 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.457 |
|
| \begin{align*}
y^{\prime }+y&=y^{4} {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| \begin{align*}
2 y^{\prime }+y&=y^{3} \left (x -1\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.537 |
|
| \begin{align*}
y^{\prime }-2 \tan \left (x \right ) y&=y^{2} \tan \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) y&=y^{3} \sec \left (x \right )^{4} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.321 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=y x +1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.320 |
|
| \begin{align*}
y y^{\prime } x -\left (x +1\right ) \sqrt {-1+y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.988 |
|
| \begin{align*}
y^{\prime }-\cot \left (x \right ) y&=y^{2} \sec \left (x \right )^{2} \\
y \left (\frac {\pi }{4}\right ) &= -1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.571 |
|
| \begin{align*}
y+\left (x^{2}-4 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.612 |
|
| \begin{align*}
y^{\prime }-\tan \left (x \right ) y&=\cos \left (x \right )-2 x \sin \left (x \right ) \\
y \left (\frac {\pi }{6}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.148 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}+2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
10.386 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=x \left (1+y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.094 |
|
| \begin{align*}
y^{\prime } x +2 y&=3 x -1 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.888 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}-y y^{\prime } x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
16.454 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{3 x -2 y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.875 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (2 x \right ) \\
y \left (\frac {\pi }{4}\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.311 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
62.239 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.231 |
|
| \begin{align*}
y^{\prime }&=\frac {x -2 y+1}{2 x -4 y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.749 |
|
| \begin{align*}
\left (-x^{3}+1\right ) y^{\prime }+x^{2} y&=x^{2} \left (-x^{3}+1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.612 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\sin \left (x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.532 |
|
| \begin{align*}
y^{\prime }+x +x y^{2}&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
4.441 |
|
| \begin{align*}
y^{\prime }+\left (\frac {1}{x}-\frac {2 x}{-x^{2}+1}\right ) y&=\frac {1}{-x^{2}+1} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.453 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=\left (x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.569 |
|
| \begin{align*}
x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.370 |
|
| \begin{align*}
\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}}&=1 \\
r \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.362 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=\cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.337 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.734 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=8 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=10 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.393 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.403 |
|
| \begin{align*}
y^{\prime \prime }+25 y&=5 x^{2}+x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.625 |
|
| \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.703 |
|
| \begin{align*}
3 y^{\prime \prime }-2 y^{\prime }-y&=2 x -3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&=8 \,{\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.656 |
|
| \begin{align*}
2 y^{\prime \prime }-7 y^{\prime }-4 y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&=54 x +18 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=100 \sin \left (4 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=4 \sinh \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.813 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=2 \cosh \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.813 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+10 y&=20-{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=2 \cos \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=x +{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.374 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+3 y&=x^{2}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.629 |
|
| \begin{align*}
y^{\prime \prime }-9 y&={\mathrm e}^{3 x}+\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.832 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+3 x&={\mathrm e}^{-3 t} \\
x \left (0\right ) &= {\frac {1}{2}} \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+5 y&=6 \sin \left (t \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=\sin \left (t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=3 \sin \left (x \right ) \\
y \left (0\right ) &= -{\frac {9}{10}} \\
y^{\prime }\left (0\right ) &= -{\frac {7}{10}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.699 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+10 y&=50 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=85 \sin \left (3 t \right ) \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= -20 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.780 |
|
| \begin{align*}
y^{\prime \prime }&=3 \sin \left (x \right )-4 y \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
\frac {x^{\prime \prime }}{2}&=-48 x \\
x \left (0\right ) &= {\frac {1}{6}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.831 |
|
| \begin{align*}
x^{\prime \prime }+5 x^{\prime }+6 x&=\cos \left (t \right ) \\
x \left (0\right ) &= {\frac {1}{10}} \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.730 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=4 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.365 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.348 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+25 y&=2 \sin \left (\frac {t}{2}\right )-\cos \left (\frac {t}{2}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+25 y&=64 \,{\mathrm e}^{-t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+25 y&=50 t^{3}-36 t^{2}-63 t +18 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.593 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=2 x \,{\mathrm e}^{-x} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.123 |
|
| \begin{align*}
y^{\prime \prime }&=9 x^{2}+2 x -1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.870 |
|
| \begin{align*}
y^{\prime \prime }-5 y&=2 \,{\mathrm e}^{5 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.412 |
|
| \begin{align*}
y^{\prime }-5 y&=\left (x -1\right ) \sin \left (x \right )+\left (x +1\right ) \cos \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.601 |
|
| \begin{align*}
y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.245 |
|
| \begin{align*}
y^{\prime }-5 y&={\mathrm e}^{x} x^{2}-x \,{\mathrm e}^{5 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.327 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x^{2}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.628 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.651 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.640 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.526 |
|
| \begin{align*}
y^{\prime }-y&=x \,{\mathrm e}^{2 x}+1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.492 |
|