|
# |
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]] |
✓ |
0.811 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
5.174 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.664 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.540 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.308 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.983 |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.732 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.136 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.086 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.658 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.602 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.383 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \delta \left (t -1\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
5.467 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.294 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.368 |
|
|
\[
{}y^{\prime \prime }+y = \frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.070 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.833 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.780 |
|
|
\[
{}y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
1.636 |
|
|
\[
{}x y^{\prime }+y = x^{2}
\] |
[_linear] |
✓ |
1.458 |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
1.482 |
|
|
\[
{}2 y^{\prime }+x \left (y^{2}-1\right ) = 0
\] |
[_separable] |
✓ |
2.076 |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.003 |
|
|
\[
{}y^{\prime } = -x
\] |
[_quadrature] |
✓ |
0.442 |
|
|
\[
{}y^{\prime } = -x \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.569 |
|
|
\[
{}y^{\prime } = \ln \left (x \right ) x
\] |
[_quadrature] |
✓ |
0.424 |
|
|
\[
{}y^{\prime } = -x \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.703 |
|
|
\[
{}y^{\prime } = x \sin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.845 |
|
|
\[
{}y^{\prime } = \tan \left (x \right )
\] |
[_quadrature] |
✓ |
1.175 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
2.088 |
|
|
\[
{}y^{\prime } = \frac {x^{2}-2 x^{2} y+2}{x^{3}}
\] |
[_linear] |
✓ |
1.642 |
|
|
\[
{}y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.535 |
|
|
\[
{}y^{\prime } = -\frac {y \left (y+1\right )}{x}
\] |
[_separable] |
✓ |
2.583 |
|
|
\[
{}y^{\prime } = a y^{\frac {a -1}{a}}
\] |
[_quadrature] |
✓ |
1.316 |
|
|
\[
{}y^{\prime } = {| y|}+1
\] |
[_quadrature] |
✓ |
2.090 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}-1+\frac {\sqrt {x^{2}+4 x +4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.851 |
|
|
\[
{}y^{\prime }+a y = 0
\] |
[_quadrature] |
✓ |
0.820 |
|
|
\[
{}y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
1.615 |
|
|
\[
{}x y^{\prime }+y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
1.878 |
|
|
\[
{}x y^{\prime }+3 y = 0
\] |
[_separable] |
✓ |
2.214 |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✓ |
1.762 |
|
|
\[
{}y^{\prime }+\frac {\left (x +1\right ) y}{x} = 0
\] |
[_separable] |
✓ |
2.191 |
|
|
\[
{}x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y = 0
\] |
[_separable] |
✓ |
2.335 |
|
|
\[
{}x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y = 0
\] |
[_separable] |
✓ |
2.600 |
|
|
\[
{}y^{\prime }-\frac {2 x y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
1.951 |
|
|
\[
{}y^{\prime }+\frac {k y}{x} = 0
\] |
[_separable] |
✓ |
1.344 |
|
|
\[
{}y^{\prime }+\tan \left (k x \right ) y = 0
\] |
[_separable] |
✓ |
2.803 |
|
|
\[
{}y^{\prime }+3 y = 1
\] |
[_quadrature] |
✓ |
1.590 |
|
|
\[
{}y^{\prime }+\left (\frac {1}{x}-1\right ) y = -\frac {2}{x}
\] |
[_linear] |
✓ |
1.243 |
|
|
\[
{}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.644 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {{\mathrm e}^{-x^{2}}}{x^{2}+1}
\] |
[_linear] |
✓ |
1.673 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {7}{x^{2}}+3
\] |
[_linear] |
✓ |
1.275 |
|
|
\[
{}y^{\prime }+\frac {4 y}{-1+x} = \frac {1}{\left (-1+x \right )^{5}}+\frac {\sin \left (x \right )}{\left (-1+x \right )^{4}}
\] |
[_linear] |
✓ |
4.993 |
|
|
\[
{}x y^{\prime }+\left (2 x^{2}+1\right ) y = x^{3} {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.922 |
|
|
\[
{}x y^{\prime }+2 y = \frac {2}{x^{2}}+1
\] |
[_linear] |
✓ |
1.289 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.872 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+2 y = \frac {\sin \left (x \right )}{x +1}
\] |
[_linear] |
✓ |
2.848 |
|
|
\[
{}\left (-2+x \right ) \left (-1+x \right ) y^{\prime }-\left (4 x -3\right ) y = \left (-2+x \right )^{3}
\] |
[_linear] |
✓ |
3.202 |
|
|
\[
{}y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y = {\mathrm e}^{-\sin \left (x \right )^{2}}
\] |
[_linear] |
✓ |
2.300 |
|
|
\[
{}x^{2} y^{\prime }+3 x y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.354 |
|
|
\[
{}y^{\prime }+7 y = {\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.676 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+4 x y = \frac {2}{x^{2}+1}
\] |
[_linear] |
✓ |
3.235 |
|
|
\[
{}x y^{\prime }+3 y = \frac {2}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
2.049 |
|
|
\[
{}y^{\prime }+\cot \left (x \right ) y = \cos \left (x \right )
\] |
[_linear] |
✓ |
2.186 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {2}{x^{2}}+1
\] |
[_linear] |
✓ |
1.382 |
|
|
\[
{}\left (-1+x \right ) y^{\prime }+3 y = \frac {1}{\left (-1+x \right )^{3}}+\frac {\sin \left (x \right )}{\left (-1+x \right )^{2}}
\] |
[_linear] |
✓ |
4.314 |
|
|
\[
{}x y^{\prime }+2 y = 8 x^{2}
\] |
[_linear] |
✓ |
2.026 |
|
|
\[
{}x y^{\prime }-2 y = -x^{2}
\] |
[_linear] |
✓ |
1.654 |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
1.950 |
|
|
\[
{}\left (-1+x \right ) y^{\prime }+3 y = \frac {1+\left (-1+x \right ) \sec \left (x \right )^{2}}{\left (-1+x \right )^{3}}
\] |
[_linear] |
✓ |
10.086 |
|
|
\[
{}\left (x +2\right ) y^{\prime }+4 y = \frac {2 x^{2}+1}{x \left (x +2\right )^{3}}
\] |
[_linear] |
✓ |
1.660 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y = x \left (x^{2}-1\right )
\] |
[_linear] |
✓ |
1.952 |
|
|
\[
{}x y^{\prime }-2 y = -1
\] |
[_separable] |
✓ |
2.415 |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime }-3 \tan \left (y\right ) = -1
\] |
[_quadrature] |
✓ |
2.165 |
|
|
\[
{}{\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right ) = \frac {1}{x^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.149 |
|
|
\[
{}\frac {x y^{\prime }}{y}+2 \ln \left (y\right ) = 4 x^{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.544 |
|
|
\[
{}\frac {y^{\prime }}{\left (y+1\right )^{2}}-\frac {1}{x \left (y+1\right )} = -\frac {3}{x^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
1.936 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+2 x +1}{-2+y}
\] |
[_separable] |
✓ |
1.930 |
|
|
\[
{}\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.681 |
|
|
\[
{}x y^{\prime }+y^{2}+y = 0
\] |
[_separable] |
✓ |
2.232 |
|
|
\[
{}\left (3 y^{3}+3 y \cos \left (y\right )+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
3.691 |
|
|
\[
{}x^{2} y y^{\prime } = \left (y^{2}-1\right )^{{3}/{2}}
\] |
[_separable] |
✓ |
8.691 |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.178 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.674 |
|
|
\[
{}y^{\prime } = \left (-1+x \right ) \left (y-1\right ) \left (-2+y\right )
\] |
[_separable] |
✓ |
3.009 |
|
|
\[
{}\left (y-1\right )^{2} y^{\prime } = 2 x +3
\] |
[_separable] |
✓ |
2.050 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+3 x +2}{-2+y}
\] |
[_separable] |
✓ |
2.398 |
|
|
\[
{}y^{\prime }+x \left (y^{2}+y\right ) = 0
\] |
[_separable] |
✓ |
2.826 |
|
|
\[
{}\left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
692.329 |
|
|
\[
{}y^{\prime }+\frac {\left (y+1\right ) \left (y-1\right ) \left (-2+y\right )}{x +1} = 0
\] |
[_separable] |
✓ |
16.816 |
|
|
\[
{}y^{\prime }+2 x \left (y+1\right ) = 0
\] |
[_separable] |
✓ |
1.925 |
|
|
\[
{}y^{\prime } = 2 x y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
11.476 |
|
|
\[
{}y^{\prime } \left (x^{2}+2\right ) = 4 x \left (y^{2}+2 y+1\right )
\] |
[_separable] |
✓ |
2.602 |
|
|
\[
{}y^{\prime } = -2 x \left (y^{3}-3 y+2\right )
\] |
[_separable] |
✓ |
4.819 |
|
|
\[
{}y^{\prime } = \frac {2 x}{2 y+1}
\] |
[_separable] |
✓ |
3.513 |
|
|
\[
{}y^{\prime } = 2 y-y^{2}
\] |
[_quadrature] |
✓ |
2.688 |
|
|
\[
{}x +y y^{\prime } = 0
\] |
[_separable] |
✓ |
4.448 |
|
|
\[
{}y^{\prime }+x^{2} \left (y+1\right ) \left (-2+y\right )^{2} = 0
\] |
[_separable] |
✓ |
3.488 |
|
|
\[
{}\left (x +1\right ) \left (-2+x \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
2.164 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
2.283 |
|