|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+4 y = \operatorname {Heaviside}\left (t -\pi \right )-\operatorname {Heaviside}\left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.354 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
1.676 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.898 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.446 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.827 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.380 |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.418 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.720 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.818 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.286 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.483 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.878 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \delta \left (t -1\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
0.518 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.748 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.827 |
|
|
\[
{}y^{\prime \prime }+y = \frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.184 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.886 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.308 |
|
|
\[
{}y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
1.495 |
|
|
\[
{}y^{\prime } x +y = x^{2}
\] |
[_linear] |
✓ |
1.796 |
|
|
\[
{}y^{\prime }+2 y x = x
\] |
[_separable] |
✓ |
3.991 |
|
|
\[
{}2 y^{\prime }+x \left (-1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
1.919 |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
1.612 |
|
|
\[
{}y^{\prime } = -x
\] |
[_quadrature] |
✓ |
0.170 |
|
|
\[
{}y^{\prime } = -x \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.352 |
|
|
\[
{}y^{\prime } = x \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.233 |
|
|
\[
{}y^{\prime } = -x \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.354 |
|
|
\[
{}y^{\prime } = x \sin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.452 |
|
|
\[
{}y^{\prime } = \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.616 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
4.810 |
|
|
\[
{}y^{\prime } = \frac {x^{2}-2 x^{2} y+2}{x^{3}}
\] |
[_linear] |
✓ |
1.305 |
|
|
\[
{}y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.144 |
|
|
\[
{}y^{\prime } = -\frac {y \left (1+y\right )}{x}
\] |
[_separable] |
✓ |
6.717 |
|
|
\[
{}y^{\prime } = a y^{\frac {a -1}{a}}
\] |
[_quadrature] |
✓ |
0.793 |
|
|
\[
{}y^{\prime } = {| y|}+1
\] |
[_quadrature] |
✓ |
2.760 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}-1+\frac {\sqrt {x^{2}+4 x +4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.853 |
|
|
\[
{}y^{\prime }+a y = 0
\] |
[_quadrature] |
✓ |
0.577 |
|
|
\[
{}y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
1.244 |
|
|
\[
{}y^{\prime } x +y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
5.288 |
|
|
\[
{}y^{\prime } x +3 y = 0
\] |
[_separable] |
✓ |
2.252 |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✓ |
1.336 |
|
|
\[
{}y^{\prime }+\frac {\left (x +1\right ) y}{x} = 0
\] |
[_separable] |
✓ |
4.584 |
|
|
\[
{}y^{\prime } x +\left (1+\frac {1}{\ln \left (x \right )}\right ) y = 0
\] |
[_separable] |
✓ |
3.130 |
|
|
\[
{}y^{\prime } x +\left (1+x \cot \left (x \right )\right ) y = 0
\] |
[_separable] |
✓ |
6.325 |
|
|
\[
{}y^{\prime }-\frac {2 x y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
1.612 |
|
|
\[
{}y^{\prime }+\frac {k y}{x} = 0
\] |
[_separable] |
✓ |
3.067 |
|
|
\[
{}y^{\prime }+\tan \left (k x \right ) y = 0
\] |
[_separable] |
✓ |
3.148 |
|
|
\[
{}y^{\prime }+3 y = 1
\] |
[_quadrature] |
✓ |
0.752 |
|
|
\[
{}y^{\prime }+\left (\frac {1}{x}-1\right ) y = -\frac {2}{x}
\] |
[_linear] |
✓ |
1.135 |
|
|
\[
{}y^{\prime }+2 y x = x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
5.126 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {{\mathrm e}^{-x^{2}}}{x^{2}+1}
\] |
[_linear] |
✓ |
1.546 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {7}{x^{2}}+3
\] |
[_linear] |
✓ |
1.049 |
|
|
\[
{}y^{\prime }+\frac {4 y}{x -1} = \frac {1}{\left (x -1\right )^{5}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{4}}
\] |
[_linear] |
✓ |
9.334 |
|
|
\[
{}y^{\prime } x +\left (2 x^{2}+1\right ) y = x^{3} {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.932 |
|
|
\[
{}y^{\prime } x +2 y = \frac {2}{x^{2}}+1
\] |
[_linear] |
✓ |
3.738 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.682 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+2 y = \frac {\sin \left (x \right )}{x +1}
\] |
[_linear] |
✓ |
6.156 |
|
|
\[
{}\left (x -2\right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y = \left (x -2\right )^{3}
\] |
[_linear] |
✓ |
5.957 |
|
|
\[
{}y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y = {\mathrm e}^{-\sin \left (x \right )^{2}}
\] |
[_linear] |
✓ |
2.378 |
|
|
\[
{}x^{2} y^{\prime }+3 y x = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.296 |
|
|
\[
{}y^{\prime }+7 y = {\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.334 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+4 y x = \frac {2}{x^{2}+1}
\] |
[_linear] |
✓ |
5.768 |
|
|
\[
{}y^{\prime } x +3 y = \frac {2}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
1.559 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) y = \cos \left (x \right )
\] |
[_linear] |
✓ |
2.048 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {2}{x^{2}}+1
\] |
[_linear] |
✓ |
1.250 |
|
|
\[
{}\left (x -1\right ) y^{\prime }+3 y = \frac {1}{\left (x -1\right )^{3}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{2}}
\] |
[_linear] |
✓ |
5.610 |
|
|
\[
{}y^{\prime } x +2 y = 8 x^{2}
\] |
[_linear] |
✓ |
5.410 |
|
|
\[
{}y^{\prime } x -2 y = -x^{2}
\] |
[_linear] |
✓ |
1.388 |
|
|
\[
{}y^{\prime }+2 y x = x
\] |
[_separable] |
✓ |
1.661 |
|
|
\[
{}\left (x -1\right ) y^{\prime }+3 y = \frac {1+\left (x -1\right ) \sec \left (x \right )^{2}}{\left (x -1\right )^{3}}
\] |
[_linear] |
✓ |
21.740 |
|
|
\[
{}\left (x +2\right ) y^{\prime }+4 y = \frac {2 x^{2}+1}{x \left (x +2\right )^{3}}
\] |
[_linear] |
✓ |
1.583 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 y x = x \left (x^{2}-1\right )
\] |
[_linear] |
✓ |
1.615 |
|
|
\[
{}y^{\prime } x -2 y = -1
\] |
[_separable] |
✓ |
6.570 |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime }-3 \tan \left (y\right ) = -1
\] |
[_quadrature] |
✓ |
1.297 |
|
|
\[
{}{\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right ) = \frac {1}{x^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
5.359 |
|
|
\[
{}\frac {x y^{\prime }}{y}+2 \ln \left (y\right ) = 4 x^{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
4.153 |
|
|
\[
{}\frac {y^{\prime }}{\left (1+y\right )^{2}}-\frac {1}{x \left (1+y\right )} = -\frac {3}{x^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
5.174 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+2 x +1}{-2+y}
\] |
[_separable] |
✓ |
2.064 |
|
|
\[
{}\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
6.125 |
|
|
\[
{}y^{\prime } x +y^{2}+y = 0
\] |
[_separable] |
✓ |
2.879 |
|
|
\[
{}\left (3 y^{3}+3 y \cos \left (y\right )+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
6.716 |
|
|
\[
{}x^{2} y y^{\prime } = \left (-1+y^{2}\right )^{{3}/{2}}
\] |
[_separable] |
✓ |
15.474 |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
1.547 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y x = 0
\] |
[_separable] |
✓ |
1.490 |
|
|
\[
{}y^{\prime } = \left (x -1\right ) \left (-1+y\right ) \left (-2+y\right )
\] |
[_separable] |
✓ |
6.648 |
|
|
\[
{}\left (-1+y\right )^{2} y^{\prime } = 2 x +3
\] |
[_separable] |
✓ |
3.107 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+3 x +2}{-2+y}
\] |
[_separable] |
✓ |
4.440 |
|
|
\[
{}y^{\prime }+x \left (y^{2}+y\right ) = 0
\] |
[_separable] |
✓ |
4.263 |
|
|
\[
{}\left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
3.926 |
|
|
\[
{}y^{\prime }+\frac {\left (1+y\right ) \left (-1+y\right ) \left (-2+y\right )}{x +1} = 0
\] |
[_separable] |
✓ |
151.338 |
|
|
\[
{}y^{\prime }+2 x \left (1+y\right ) = 0
\] |
[_separable] |
✓ |
1.666 |
|
|
\[
{}y^{\prime } = 2 x y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
13.185 |
|
|
\[
{}y^{\prime } \left (x^{2}+2\right ) = 4 x \left (y^{2}+2 y+1\right )
\] |
[_separable] |
✓ |
2.725 |
|
|
\[
{}y^{\prime } = -2 x \left (y^{3}-3 y+2\right )
\] |
[_separable] |
✓ |
18.582 |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
8.584 |
|
|
\[
{}y^{\prime } = 2 y-y^{2}
\] |
[_quadrature] |
✓ |
2.578 |
|
|
\[
{}x +y y^{\prime } = 0
\] |
[_separable] |
✓ |
11.622 |
|
|
\[
{}y^{\prime }+x^{2} \left (1+y\right ) \left (-2+y\right )^{2} = 0
\] |
[_separable] |
✓ |
7.430 |
|
|
\[
{}\left (x +1\right ) \left (x -2\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
2.392 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
4.932 |
|