|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.236 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.248 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.243 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.606 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
44.115 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
72.089 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
27.058 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.728 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.529 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.833 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
33.429 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.167 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.944 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
24.937 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
28.787 |
|
|
\[
{}y^{\prime \prime }+9 y = \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.500 |
|
|
\[
{}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.783 |
|
|
\[
{}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.319 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.943 |
|
|
\[
{}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.839 |
|
|
\[
{}y^{\prime \prime }+4 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.341 |
|
|
\[
{}y^{\prime \prime }-4 y = {\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.303 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.355 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.565 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.372 |
|
|
\[
{}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.658 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.807 |
|
|
\[
{}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.695 |
|
|
\[
{}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.328 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.495 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.483 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (t -1\right )-3 \delta \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.567 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+2 y = {\mathrm e}^{-2 t} \sin \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.505 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.740 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.772 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.860 |
|
|
\[
{}y^{\prime \prime }+16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.342 |
|
|
\[
{}y^{\prime \prime }+4 y = \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.345 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.292 |
|
|
\[
{}y^{\prime \prime }+16 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.375 |
|
|
\[
{}y^{\prime } = 3-\sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.298 |
|
|
\[
{}y^{\prime } = 3-\sin \left (y\right )
\] |
[_quadrature] |
✓ |
0.591 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.947 |
|
|
\[
{}y^{\prime } x = \arcsin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
20.120 |
|
|
\[
{}y y^{\prime } = 2 x
\] |
[_separable] |
✓ |
2.722 |
|
|
\[
{}y^{\prime \prime } = \frac {x +1}{x -1}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.346 |
|
|
\[
{}x^{2} y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.744 |
|
|
\[
{}y^{2} y^{\prime \prime } = 8 x^{2}
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.083 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+8 y = {\mathrm e}^{-x^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.892 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.740 |
|
|
\[
{}y^{\prime } = 4 x^{3}
\] |
[_quadrature] |
✓ |
0.218 |
|
|
\[
{}y^{\prime } = 20 \,{\mathrm e}^{-4 x}
\] |
[_quadrature] |
✓ |
0.281 |
|
|
\[
{}y^{\prime } x +\sqrt {x} = 2
\] |
[_quadrature] |
✓ |
0.299 |
|
|
\[
{}\sqrt {x +4}\, y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.345 |
|
|
\[
{}y^{\prime } = x \cos \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.303 |
|
|
\[
{}y^{\prime } = x \cos \left (x \right )
\] |
[_quadrature] |
✓ |
0.301 |
|
|
\[
{}x = \left (x^{2}-9\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
0.341 |
|
|
\[
{}1 = \left (x^{2}-9\right ) y^{\prime }
\] |
[_quadrature] |
✓ |
0.370 |
|
|
\[
{}1 = x^{2}-9 y^{\prime }
\] |
[_quadrature] |
✓ |
0.256 |
|
|
\[
{}y^{\prime \prime } = \sin \left (2 x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.441 |
|
|
\[
{}y^{\prime \prime }-3 = x
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.148 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 1
\] |
[[_high_order, _quadrature]] |
✓ |
0.095 |
|
|
\[
{}y^{\prime } = 40 x \,{\mathrm e}^{2 x}
\] |
[_quadrature] |
✓ |
0.418 |
|
|
\[
{}\left (x +6\right )^{{1}/{3}} y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.585 |
|
|
\[
{}y^{\prime } = \frac {x -1}{x +1}
\] |
[_quadrature] |
✓ |
0.444 |
|
|
\[
{}y^{\prime } x +2 = \sqrt {x}
\] |
[_quadrature] |
✓ |
0.530 |
|
|
\[
{}y^{\prime } \cos \left (x \right )-\sin \left (x \right ) = 0
\] |
[_quadrature] |
✓ |
0.851 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1
\] |
[_quadrature] |
✓ |
0.467 |
|
|
\[
{}x y^{\prime \prime }+2 = \sqrt {x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.436 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {x}{2}\right )
\] |
[_quadrature] |
✓ |
0.294 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {x}{2}\right )
\] |
[_quadrature] |
✓ |
0.443 |
|
|
\[
{}y^{\prime } = \sin \left (\frac {x}{2}\right )
\] |
[_quadrature] |
✓ |
0.428 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.269 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.501 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.432 |
|
|
\[
{}y^{\prime } = 3 \sqrt {x +3}
\] |
[_quadrature] |
✓ |
0.495 |
|
|
\[
{}y^{\prime } = x \,{\mathrm e}^{-x^{2}}
\] |
[_quadrature] |
✓ |
0.405 |
|
|
\[
{}y^{\prime } = \frac {x}{\sqrt {x^{2}+5}}
\] |
[_quadrature] |
✓ |
0.713 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{2}+1}
\] |
[_quadrature] |
✓ |
0.437 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{-9 x^{2}}
\] |
[_quadrature] |
✓ |
0.433 |
|
|
\[
{}y^{\prime } x = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.474 |
|
|
\[
{}y^{\prime } x = \sin \left (x^{2}\right )
\] |
[_quadrature] |
✓ |
0.502 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & x <0 \\ 1 & 0\le x \end {array}\right .
\] |
[_quadrature] |
✓ |
0.254 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x \end {array}\right .
\] |
[_quadrature] |
✓ |
0.260 |
|
|
\[
{}y^{\prime } = \left \{\begin {array}{cc} 0 & x <1 \\ 1 & 1\le x <2 \\ 0 & 2\le x \end {array}\right .
\] |
[_quadrature] |
✓ |
0.275 |
|
|
\[
{}y^{\prime }+3 y x = 6 x
\] |
[_separable] |
✓ |
0.996 |
|
|
\[
{}\sin \left (x +y\right )-y y^{\prime } = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.732 |
|
|
\[
{}y^{\prime }-y^{3} = 8
\] |
[_quadrature] |
✓ |
1.566 |
|
|
\[
{}x^{2} y^{\prime }+x y^{2} = x
\] |
[_separable] |
✓ |
1.250 |
|
|
\[
{}y^{\prime }-y^{2} = x
\] |
[[_Riccati, _special]] |
✓ |
0.895 |
|
|
\[
{}y^{3}-25 y+y^{\prime } = 0
\] |
[_quadrature] |
✓ |
1.266 |
|
|
\[
{}\left (x -2\right ) y^{\prime } = 3+y
\] |
[_separable] |
✓ |
1.310 |
|
|
\[
{}\left (y-2\right ) y^{\prime } = x -3
\] |
[_separable] |
✓ |
2.525 |
|
|
\[
{}y^{\prime }+2 y-y^{2} = -2
\] |
[_quadrature] |
✓ |
0.401 |
|
|
\[
{}y^{\prime }+\left (8-x \right ) y-y^{2} = -8 x
\] |
[_Riccati] |
✓ |
1.461 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
0.677 |
|
|
\[
{}y^{\prime } = 3 y^{2}-y^{2} \sin \left (x \right )
\] |
[_separable] |
✓ |
1.802 |
|
|
\[
{}y^{\prime } = 3 x -y \sin \left (x \right )
\] |
[_linear] |
✓ |
1.773 |
|
|
\[
{}y^{\prime } x = \left (x -y\right )^{2}
\] |
[_rational, _Riccati] |
✓ |
1.418 |
|
|
\[
{}y^{\prime } = \sqrt {x^{2}+1}
\] |
[_quadrature] |
✓ |
0.314 |
|