|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.496 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.501 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.958 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.047 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.805 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.347 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 5
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.411 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.214 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 10
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.351 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+6 y = -8
\] |
[[_2nd_order, _missing_x]] |
✓ |
7.277 |
|
|
\[
{}y^{\prime \prime }+9 y = {\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.604 |
|
|
\[
{}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.444 |
|
|
\[
{}y^{\prime \prime }+2 y = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.466 |
|
|
\[
{}y^{\prime \prime }+4 y = {\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.409 |
|
|
\[
{}y^{\prime \prime }+9 y = 6
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.383 |
|
|
\[
{}y^{\prime \prime }+2 y = -{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.405 |
|
|
\[
{}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.049 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 3 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.087 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 3 t +2
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.275 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.325 |
|
|
\[
{}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.185 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.290 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.271 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.333 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.319 |
|
|
\[
{}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.835 |
|
|
\[
{}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.081 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.531 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.547 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.650 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.589 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.607 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.701 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
30.125 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
50.378 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
28.754 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.776 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.602 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.796 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
32.392 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.883 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.478 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
40.233 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.004 |
|
|
\[
{}y^{\prime \prime }+9 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.021 |
|
|
\[
{}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.271 |
|
|
\[
{}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.942 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.321 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.862 |
|
|
\[
{}y^{\prime \prime }+4 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.312 |
|
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.260 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.326 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.040 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.319 |
|
|
\[
{}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.032 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.844 |
|
|
\[
{}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.077 |
|
|
\[
{}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.533 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.898 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.000 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.880 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.477 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.855 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.138 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.102 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.300 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.325 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.231 |
|
|
\[
{}y^{\prime \prime }+16 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.317 |
|
|
\[
{}y^{\prime } = 3-\sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.526 |
|
|
\[
{}y^{\prime } = 3-\sin \left (y\right )
\] |
[_quadrature] |
✓ |
1.447 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.271 |
|
|
\[
{}y^{\prime } x = \arcsin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
19.045 |
|
|
\[
{}y^{\prime } y = 2 x
\] |
[_separable] |
✓ |
3.482 |
|
|
\[
{}y^{\prime \prime } = \frac {x +1}{x -1}
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.135 |
|
|
\[
{}x^{2} y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.668 |
|
|
\[
{}y^{2} y^{\prime \prime } = 8 x^{2}
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.132 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
25.605 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.782 |
|
|
\[
{}y^{\prime } = 4 x^{3}
\] |
[_quadrature] |
✓ |
0.449 |
|
|
\[
{}y^{\prime } = 20 \,{\mathrm e}^{-4 x}
\] |
[_quadrature] |
✓ |
0.512 |
|
|
\[
{}y^{\prime } x +\sqrt {x} = 2
\] |
[_quadrature] |
✓ |
0.455 |
|
|
\[
{}\sqrt {x +4}\, y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.574 |
|
|
\[
{}y^{\prime } = x \cos \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.539 |
|
|
\[
{}y^{\prime } = x \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.523 |
|
|
\[
{}x = \left (x^{2}-9\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
0.546 |
|
|
\[
{}1 = \left (x^{2}-9\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
0.599 |
|
|
\[
{}1 = x^{2}-9 y^{\prime }
\] |
[_quadrature] |
✓ |
0.480 |
|
|
\[
{}y^{\prime \prime } = \sin \left (2 x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.216 |
|
|
\[
{}y^{\prime \prime }-3 = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.933 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _quadrature]] |
✓ |
0.106 |
|
|
\[
{}y^{\prime } = 40 x \,{\mathrm e}^{2 x}
\] |
[_quadrature] |
✓ |
0.710 |
|
|
\[
{}\left (x +6\right )^{{1}/{3}} y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.606 |
|
|
\[
{}y^{\prime } = \frac {x -1}{x +1}
\] |
[_quadrature] |
✓ |
0.770 |
|
|
\[
{}y^{\prime } x +2 = \sqrt {x}
\] |
[_quadrature] |
✓ |
0.804 |
|
|
\[
{}y^{\prime } \cos \left (x \right )-\sin \left (x \right ) = 0
\] |
[_quadrature] |
✓ |
1.180 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.791 |
|
|
\[
{}x y^{\prime \prime }+2 = \sqrt {x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.569 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {x}{2}\right )
\] |
[_quadrature] |
✓ |
0.521 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {x}{2}\right )
\] |
[_quadrature] |
✓ |
0.743 |
|