|
# |
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]] |
✓ |
0.560 |
|
|
\[
{}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 1-\operatorname {Heaviside}\left (t -\pi \right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
2.171 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = k \left (\operatorname {Heaviside}\left (t -\frac {3}{2}\right )-\operatorname {Heaviside}\left (t -\frac {5}{2}\right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.049 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -\frac {3}{2}\right )}{2}-\frac {\operatorname {Heaviside}\left (t -\frac {5}{2}\right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.233 |
|
|
\[
{}u^{\prime \prime }+\frac {u^{\prime }}{4}+u = \frac {\operatorname {Heaviside}\left (t -5\right ) \left (t -5\right )-\operatorname {Heaviside}\left (t -5-k \right ) \left (t -5-k \right )}{k}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.733 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.744 |
|
|
\[
{}y^{\prime \prime }+4 y = \delta \left (t -\pi \right )-\delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.497 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \delta \left (t -5\right )+\operatorname {Heaviside}\left (t -10\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.656 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \sin \left (t \right )+\delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.673 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right ) \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.511 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.456 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \cos \left (t \right )+\delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.144 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = \delta \left (t -1\right )
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
2.056 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{2}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.864 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{4}+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.816 |
|
|
\[
{}y^{\prime \prime }+y = \frac {\operatorname {Heaviside}\left (t -4+k \right )-\operatorname {Heaviside}\left (t -4-k \right )}{2 k}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.536 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.086 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = \delta \left (t -\pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.531 |
|
|
\[
{}y^{\prime } = 2 y
\] |
[_quadrature] |
✓ |
1.137 |
|
|
\[
{}x y^{\prime }+y = x^{2}
\] |
[_linear] |
✓ |
1.270 |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
1.191 |
|
|
\[
{}2 y^{\prime }+x \left (y^{2}-1\right ) = 0
\] |
[_separable] |
✓ |
2.045 |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
3.339 |
|
|
\[
{}y^{\prime } = -x
\] |
[_quadrature] |
✓ |
0.266 |
|
|
\[
{}y^{\prime } = -x \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.370 |
|
|
\[
{}y^{\prime } = x \ln \left (x \right )
\] |
[_quadrature] |
✓ |
0.330 |
|
|
\[
{}y^{\prime } = -x \,{\mathrm e}^{x}
\] |
[_quadrature] |
✓ |
0.515 |
|
|
\[
{}y^{\prime } = x \sin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.725 |
|
|
\[
{}y^{\prime } = \tan \left (x \right )
\] |
[_quadrature] |
✓ |
0.966 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
1.970 |
|
|
\[
{}y^{\prime } = \frac {x^{2}-2 x^{2} y+2}{x^{3}}
\] |
[_linear] |
✓ |
1.424 |
|
|
\[
{}y^{\prime } = x \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.507 |
|
|
\[
{}y^{\prime } = -\frac {y \left (y+1\right )}{x}
\] |
[_separable] |
✓ |
2.246 |
|
|
\[
{}y^{\prime } = a y^{\frac {a -1}{a}}
\] |
[_quadrature] |
✓ |
1.069 |
|
|
\[
{}y^{\prime } = {| y|}+1
\] |
[_quadrature] |
✓ |
1.289 |
|
|
\[
{}y^{\prime } = -\frac {x}{2}-1+\frac {\sqrt {x^{2}+4 x +4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
1.849 |
|
|
\[
{}y^{\prime }+a y = 0
\] |
[_quadrature] |
✓ |
0.773 |
|
|
\[
{}y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
1.237 |
|
|
\[
{}x y^{\prime }+y \ln \left (x \right ) = 0
\] |
[_separable] |
✓ |
1.468 |
|
|
\[
{}3 y+x y^{\prime } = 0
\] |
[_separable] |
✓ |
1.789 |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✓ |
1.428 |
|
|
\[
{}y^{\prime }+\frac {\left (x +1\right ) y}{x} = 0
\] |
[_separable] |
✓ |
1.815 |
|
|
\[
{}x y^{\prime }+\left (1+\frac {1}{\ln \left (x \right )}\right ) y = 0
\] |
[_separable] |
✓ |
2.060 |
|
|
\[
{}x y^{\prime }+\left (1+x \cot \left (x \right )\right ) y = 0
\] |
[_separable] |
✓ |
2.464 |
|
|
\[
{}y^{\prime }-\frac {2 x y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
1.683 |
|
|
\[
{}y^{\prime }+\frac {k y}{x} = 0
\] |
[_separable] |
✓ |
1.641 |
|
|
\[
{}y^{\prime }+\tan \left (k x \right ) y = 0
\] |
[_separable] |
✓ |
2.072 |
|
|
\[
{}y^{\prime }+3 y = 1
\] |
[_quadrature] |
✓ |
1.107 |
|
|
\[
{}y^{\prime }+\left (\frac {1}{x}-1\right ) y = -\frac {2}{x}
\] |
[_linear] |
✓ |
1.153 |
|
|
\[
{}y^{\prime }+2 x y = x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.426 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {{\mathrm e}^{-x^{2}}}{x^{2}+1}
\] |
[_linear] |
✓ |
1.542 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {7}{x^{2}}+3
\] |
[_linear] |
✓ |
1.056 |
|
|
\[
{}y^{\prime }+\frac {4 y}{x -1} = \frac {1}{\left (x -1\right )^{5}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{4}}
\] |
[_linear] |
✓ |
4.945 |
|
|
\[
{}x y^{\prime }+\left (2 x^{2}+1\right ) y = x^{3} {\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.756 |
|
|
\[
{}2 y+x y^{\prime } = \frac {2}{x^{2}}+1
\] |
[_linear] |
✓ |
1.088 |
|
|
\[
{}y^{\prime }+y \tan \left (x \right ) = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.713 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+2 y = \frac {\sin \left (x \right )}{x +1}
\] |
[_linear] |
✓ |
2.760 |
|
|
\[
{}\left (-2+x \right ) \left (x -1\right ) y^{\prime }-\left (4 x -3\right ) y = \left (-2+x \right )^{3}
\] |
[_linear] |
✓ |
3.063 |
|
|
\[
{}y^{\prime }+2 \sin \left (x \right ) \cos \left (x \right ) y = {\mathrm e}^{-\sin \left (x \right )^{2}}
\] |
[_linear] |
✓ |
2.071 |
|
|
\[
{}x^{2} y^{\prime }+3 x y = {\mathrm e}^{x}
\] |
[_linear] |
✓ |
1.241 |
|
|
\[
{}y^{\prime }+7 y = {\mathrm e}^{3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.419 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+4 x y = \frac {2}{x^{2}+1}
\] |
[_linear] |
✓ |
3.094 |
|
|
\[
{}3 y+x y^{\prime } = \frac {2}{x \left (x^{2}+1\right )}
\] |
[_linear] |
✓ |
1.895 |
|
|
\[
{}\cot \left (x \right ) y+y^{\prime } = \cos \left (x \right )
\] |
[_linear] |
✓ |
2.054 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \frac {2}{x^{2}}+1
\] |
[_linear] |
✓ |
1.235 |
|
|
\[
{}\left (x -1\right ) y^{\prime }+3 y = \frac {1}{\left (x -1\right )^{3}}+\frac {\sin \left (x \right )}{\left (x -1\right )^{2}}
\] |
[_linear] |
✓ |
4.263 |
|
|
\[
{}2 y+x y^{\prime } = 8 x^{2}
\] |
[_linear] |
✓ |
1.902 |
|
|
\[
{}x y^{\prime }-2 y = -x^{2}
\] |
[_linear] |
✓ |
1.368 |
|
|
\[
{}y^{\prime }+2 x y = x
\] |
[_separable] |
✓ |
1.562 |
|
|
\[
{}\left (x -1\right ) y^{\prime }+3 y = \frac {1+\left (x -1\right ) \sec \left (x \right )^{2}}{\left (x -1\right )^{3}}
\] |
[_linear] |
✓ |
10.115 |
|
|
\[
{}\left (x +2\right ) y^{\prime }+4 y = \frac {2 x^{2}+1}{x \left (x +2\right )^{3}}
\] |
[_linear] |
✓ |
1.595 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y = x \left (x^{2}-1\right )
\] |
[_linear] |
✓ |
1.742 |
|
|
\[
{}x y^{\prime }-2 y = -1
\] |
[_separable] |
✓ |
2.291 |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime }-3 \tan \left (y\right ) = -1
\] |
[_quadrature] |
✓ |
476.183 |
|
|
\[
{}{\mathrm e}^{y^{2}} \left (2 y y^{\prime }+\frac {2}{x}\right ) = \frac {1}{x^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
1.826 |
|
|
\[
{}\frac {x y^{\prime }}{y}+2 \ln \left (y\right ) = 4 x^{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.549 |
|
|
\[
{}\frac {y^{\prime }}{\left (y+1\right )^{2}}-\frac {1}{x \left (y+1\right )} = -\frac {3}{x^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
1.824 |
|
|
\[
{}y^{\prime } = \frac {3 x^{2}+2 x +1}{y-2}
\] |
[_separable] |
✓ |
1.538 |
|
|
\[
{}\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.960 |
|
|
\[
{}x y^{\prime }+y^{2}+y = 0
\] |
[_separable] |
✓ |
1.685 |
|
|
\[
{}\left (3 y^{3}+3 y \cos \left (y\right )+1\right ) y^{\prime }+\frac {\left (2 x +1\right ) y}{x^{2}+1} = 0
\] |
[_separable] |
✓ |
2.820 |
|
|
\[
{}x^{2} y y^{\prime } = \left (y^{2}-1\right )^{{3}/{2}}
\] |
[_separable] |
✓ |
7.102 |
|
|
\[
{}y^{\prime } = x^{2} \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
3.140 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.316 |
|
|
\[
{}y^{\prime } = \left (x -1\right ) \left (y-1\right ) \left (y-2\right )
\] |
[_separable] |
✓ |
2.701 |
|
|
\[
{}\left (y-1\right )^{2} y^{\prime } = 2 x +3
\] |
[_separable] |
✓ |
1.841 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+3 x +2}{y-2}
\] |
[_separable] |
✓ |
2.192 |
|
|
\[
{}y^{\prime }+x \left (y^{2}+y\right ) = 0
\] |
[_separable] |
✓ |
2.207 |
|
|
\[
{}\left (3 y^{2}+4 y\right ) y^{\prime }+2 x +\cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
181.736 |
|
|
\[
{}y^{\prime }+\frac {\left (y+1\right ) \left (y-1\right ) \left (y-2\right )}{x +1} = 0
\] |
[_separable] |
✓ |
9.549 |
|
|
\[
{}y^{\prime }+2 x \left (y+1\right ) = 0
\] |
[_separable] |
✓ |
1.446 |
|
|
\[
{}y^{\prime } = 2 x y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
8.292 |
|
|
\[
{}y^{\prime } \left (x^{2}+2\right ) = 4 x \left (y^{2}+2 y+1\right )
\] |
[_separable] |
✓ |
2.515 |
|
|
\[
{}y^{\prime } = -2 x \left (y^{3}-3 y+2\right )
\] |
[_separable] |
✓ |
4.161 |
|
|
\[
{}y^{\prime } = \frac {2 x}{1+2 y}
\] |
[_separable] |
✓ |
3.226 |
|
|
\[
{}y^{\prime } = 2 y-y^{2}
\] |
[_quadrature] |
✓ |
2.263 |
|
|
\[
{}x +y y^{\prime } = 0
\] |
[_separable] |
✓ |
4.347 |
|
|
\[
{}y^{\prime }+x^{2} \left (y+1\right ) \left (y-2\right )^{2} = 0
\] |
[_separable] |
✓ |
2.960 |
|
|
\[
{}\left (x +1\right ) \left (-2+x \right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
1.829 |
|
|
\[
{}y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
1.801 |
|