|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.381 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.434 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.377 |
|
|
\[
{}y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.633 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 18
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.671 |
|
|
\[
{}y^{\prime \prime }-y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.846 |
|
|
\[
{}y^{\prime \prime }-4 y = 32 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.225 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = -2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.602 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 3 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.717 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.566 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.397 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+25 y = -1
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.947 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = -{\mathrm e}^{3 t}-2 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
3.016 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = -3 t -4 t^{2} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.121 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 2 t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.775 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.466 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.948 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.385 |
|
|
\[
{}y^{\prime \prime }+9 \pi ^{2} y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
117.997 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.538 |
|
|
\[
{}y^{\prime }-4 y = t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.386 |
|
|
\[
{}y^{\prime }+y = \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.871 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.767 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{-4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.591 |
|
|
\[
{}y^{\prime }+4 y = t \,{\mathrm e}^{-4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.968 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.713 |
|
|
\[
{}x^{\prime \prime }+9 x = \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.973 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+37 y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.902 |
|
|
\[
{}y^{\prime \prime }+4 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.750 |
|
|
\[
{}y^{\prime \prime }+16 y^{\prime } = t
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.263 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.196 |
|
|
\[
{}y^{\prime \prime }+16 y = 2 \cos \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.974 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 2 t \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.220 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{4} = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.031 |
|
|
\[
{}y^{\prime \prime }+16 y = \csc \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.780 |
|
|
\[
{}y^{\prime \prime }+16 y = \cot \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.862 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+50 y = {\mathrm e}^{-t} \csc \left (7 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
90.547 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+25 y = {\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
54.234 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+26 y = {\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
73.198 |
|
|
\[
{}y^{\prime \prime }+12 y^{\prime }+37 y = {\mathrm e}^{-6 t} \csc \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
33.243 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+34 y = {\mathrm e}^{3 t} \tan \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
47.358 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+34 y = {\mathrm e}^{5 t} \cot \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
36.240 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+37 y = {\mathrm e}^{6 t} \sec \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
31.140 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 t} \sec \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
29.794 |
|
|
\[
{}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.406 |
|
|
\[
{}y^{\prime \prime }-25 y = \frac {1}{1-{\mathrm e}^{5 t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.521 |
|
|
\[
{}y^{\prime \prime }-y = 2 \sinh \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.737 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.335 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.352 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{4}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.351 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 t}}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.354 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.403 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{t}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.628 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t} \sqrt {-t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.554 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \sqrt {-t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.530 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 t} \ln \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.490 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 t} \arctan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.595 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.103 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.211 |
|
|
\[
{}y^{\prime \prime }+9 y = \tan \left (3 t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.482 |
|
|
\[
{}y^{\prime \prime }+9 y = \sec \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.664 |
|
|
\[
{}y^{\prime \prime }+9 y = \tan \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.523 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
8.395 |
|
|
\[
{}y^{\prime \prime }+16 y = \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.905 |
|
|
\[
{}y^{\prime \prime }+4 y = \tan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.373 |
|
|
\[
{}y^{\prime \prime }+9 y = \sec \left (3 t \right ) \tan \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.773 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (2 t \right ) \tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.757 |
|
|
\[
{}y^{\prime \prime }+9 y = \frac {\csc \left (3 t \right )}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.398 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (2 t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
10.015 |
|
|
\[
{}y^{\prime \prime }-16 y = 16 t \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.009 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (t \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.684 |
|
|
\[
{}y^{\prime \prime }+4 y = \sec \left (2 t \right )+\tan \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
5.849 |
|
|
\[
{}y^{\prime \prime }+9 y = \csc \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.246 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 65 \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.500 |
|
|
\[
{}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = \ln \left (t \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.768 |
|
|
\[
{}t^{2} y^{\prime \prime }+t y^{\prime }+4 y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.157 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 2 \ln \left (t \right )
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.832 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+y = {\mathrm e}^{-\frac {t}{2}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.327 |
|
|
\[
{}y^{\prime \prime }+4 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.822 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.153 |
|
|
\[
{}t^{2} y^{\prime \prime }-4 t y^{\prime }+\left (t^{2}+6\right ) y = t^{3}+2 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.941 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+t y = 0
\] |
[_Lienard] |
✓ |
0.149 |
|
|
\[
{}t y^{\prime \prime }+2 y^{\prime }+t y = -t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.874 |
|
|
\[
{}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.157 |
|
|
\[
{}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (16 t^{2}-1\right ) y = 16 t^{{3}/{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.240 |
|
|
\[
{}t^{2} \left (\ln \left (t \right )-1\right ) y^{\prime \prime }-t y^{\prime }+y = -\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.515 |
|
|
\[
{}\left (\sin \left (t \right )-t \cos \left (t \right )\right ) y^{\prime \prime }-t \sin \left (t \right ) y^{\prime }+\sin \left (t \right ) y = t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
11.208 |
|
|
\[
{}y^{\prime \prime \prime } = 0
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.043 |
|
|
\[
{}y^{\prime \prime \prime }-10 y^{\prime \prime }+25 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.052 |
|
|
\[
{}8 y^{\prime \prime \prime }+y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.049 |
|
|
\[
{}y^{\prime \prime \prime \prime }+16 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.054 |
|
|
\[
{}3 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}6 y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.054 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime }+2 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.056 |
|
|
\[
{}5 y^{\prime \prime \prime }-15 y^{\prime }+11 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.105 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.050 |
|
|
\[
{}y^{\prime \prime \prime \prime }-9 y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.051 |
|
|
\[
{}y^{\prime \prime \prime \prime }-16 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.059 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }-y^{\prime \prime }+54 y^{\prime }-72 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.065 |
|