|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = F \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.214 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = F \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.685 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }-12 y = F \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.757 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 5 x \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.115 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.088 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = 4 \ln \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
5.995 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y = \cos \left (x \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
3.931 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +9 y = 9 \ln \left (x \right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
54.533 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +5 y = 8 x \ln \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
63.049 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x^{4} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
19.542 |
|
|
\[
{}x^{2} y^{\prime \prime }+6 y^{\prime } x +6 y = 4 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.970 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = \frac {x^{2}}{\ln \left (x \right )}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.892 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.014 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
4.280 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+25 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
5.144 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.091 |
|
|
\[
{}x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.097 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.356 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[_Gegenbauer] |
✓ |
0.101 |
|
|
\[
{}y^{\prime \prime }-\frac {y^{\prime }}{x}+4 x^{2} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.149 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (4 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.097 |
|
|
\[
{}y^{\prime \prime }+y = \csc \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.247 |
|
|
\[
{}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 8 x^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.249 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 8 x^{4}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.203 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = 15 \,{\mathrm e}^{3 x} \sqrt {x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.242 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = 4 \,{\mathrm e}^{2 x} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.248 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = \sqrt {x}\, \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.200 |
|
|
\[
{}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.043 |
|
|
\[
{}y^{\prime \prime \prime }+11 y^{\prime \prime }+36 y^{\prime }+26 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.057 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-3 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.717 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 4 \,{\mathrm e}^{-2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.668 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = x^{2}
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.122 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+25 y^{\prime } = \sin \left (4 x \right )
\] |
[[_3rd_order, _missing_y]] |
✓ |
0.149 |
|
|
\[
{}y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y = 8 \,{\mathrm e}^{-x}+1
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.141 |
|
|
\[
{}y^{\prime \prime }-4 y = 5 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.724 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.717 |
|
|
\[
{}y^{\prime \prime }-y = 4 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.677 |
|
|
\[
{}y^{\prime \prime }+y x = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.513 |
|
|
\[
{}y^{\prime \prime }+4 y = \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
79.511 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 5 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.814 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.902 |
|
|
\[
{}y^{\prime \prime }+y = 4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.291 |
|
|
\[
{}y^{\prime }-2 y = 6 \,{\mathrm e}^{5 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.339 |
|
|
\[
{}y^{\prime }+y = 8 \,{\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.020 |
|
|
\[
{}y^{\prime }+3 y = 2 \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.365 |
|
|
\[
{}y^{\prime }+2 y = 4 t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.340 |
|
|
\[
{}y^{\prime }-y = 6 \cos \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.599 |
|
|
\[
{}y^{\prime }-y = 5 \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.585 |
|
|
\[
{}y^{\prime }+y = 5 \,{\mathrm e}^{t} \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.603 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.333 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.757 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.750 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 36
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.446 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 10 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.415 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.313 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 30 \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.427 |
|
|
\[
{}y^{\prime \prime }-y = 12 \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.378 |
|
|
\[
{}y^{\prime \prime }+4 y = 10 \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 12-6 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.404 |
|
|
\[
{}y^{\prime \prime }-y = 6 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.447 |
|
|
\[
{}y^{\prime \prime }-9 y = 13 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.400 |
|
|
\[
{}y^{\prime \prime }-y = 8 \sin \left (t \right )-6 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.490 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 10 \cos \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.503 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.694 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+4 y = 20 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.430 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 3 \cos \left (t \right )+\sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.825 |
|
|
\[
{}y^{\prime \prime }+4 y = 9 \sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.530 |
|
|
\[
{}y^{\prime \prime }+y = 6 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.681 |
|
|
\[
{}y^{\prime \prime }+9 y = 7 \sin \left (4 t \right )+14 \cos \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.010 |
|
|
\[
{}y^{\prime \prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.427 |
|
|
\[
{}y^{\prime }+2 y = 2 \operatorname {Heaviside}\left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.773 |
|
|
\[
{}y^{\prime }-2 y = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.448 |
|
|
\[
{}y^{\prime }-y = 4 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \sin \left (t +\frac {\pi }{4}\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.750 |
|
|
\[
{}y^{\prime }+2 y = \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.736 |
|
|
\[
{}y^{\prime }+3 y = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.691 |
|
|
\[
{}y^{\prime }-3 y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
1.044 |
|
|
\[
{}y^{\prime }-3 y = -10 \,{\mathrm e}^{-t +a} \sin \left (-2 t +2 a \right ) \operatorname {Heaviside}\left (t -a \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.048 |
|
|
\[
{}y^{\prime \prime }-y = \operatorname {Heaviside}\left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.542 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 1-3 \operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.234 |
|
|
\[
{}y^{\prime \prime }-4 y = \operatorname {Heaviside}\left (t -1\right )-\operatorname {Heaviside}\left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.579 |
|
|
\[
{}y^{\prime \prime }+y = t -\operatorname {Heaviside}\left (t -1\right ) \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.528 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = -10 \operatorname {Heaviside}\left (t -\frac {\pi }{4}\right ) \cos \left (t +\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.678 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 30 \operatorname {Heaviside}\left (t -1\right ) {\mathrm e}^{1-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.004 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = 5 \operatorname {Heaviside}\left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.360 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.875 |
|
|
\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.561 |
|
|
\[
{}y^{\prime }-y = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.266 |
|
|
\[
{}y^{\prime }+y = \delta \left (t -5\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.688 |
|
|
\[
{}y^{\prime }-2 y = \delta \left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.356 |
|
|
\[
{}y^{\prime }+4 y = 3 \delta \left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.509 |
|
|
\[
{}y^{\prime }-5 y = 2 \,{\mathrm e}^{-t}+\delta \left (t -3\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.598 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.294 |
|
|
\[
{}y^{\prime \prime }-4 y = \delta \left (t -3\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.685 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -\frac {\pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.463 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.876 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = \delta \left (t -2\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.009 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+13 y = \delta \left (t -\frac {\pi }{4}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.246 |
|
|
\[
{}y^{\prime \prime }+9 y = 15 \sin \left (2 t \right )+\delta \left (t -\frac {\pi }{6}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.698 |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \cos \left (3 t \right )+\delta \left (t -\frac {\pi }{3}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.003 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \sin \left (t \right )+\delta \left (t -\frac {\pi }{6}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.450 |
|