|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.421 |
|
|
\[
{}3 t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.089 |
|
|
\[
{}t^{2} y^{\prime \prime }-t y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.021 |
|
|
\[
{}a y^{\prime \prime }+2 b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.096 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.075 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.719 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }-16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.728 |
|
|
\[
{}y^{\prime \prime }-16 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.927 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.349 |
|
|
\[
{}{y^{\prime \prime }}^{2}-5 y^{\prime \prime } y^{\prime }+4 y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.070 |
|
|
\[
{}{y^{\prime \prime }}^{2}-2 y^{\prime \prime } y^{\prime }+y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.082 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.810 |
|
|
\[
{}y^{\prime \prime }+y = 8 \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.726 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = -{\mathrm e}^{-9 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.950 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 2 \,{\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.011 |
|
|
\[
{}y^{\prime \prime }-y = 2 t -4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.943 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.969 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = 3-4 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.569 |
|
|
\[
{}y^{\prime \prime }+y = \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.017 |
|
|
\[
{}y^{\prime \prime }+4 y = 4 \cos \left (t \right )-\sin \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.991 |
|
|
\[
{}y^{\prime \prime }+4 y = \cos \left (2 t \right )+t
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.560 |
|
|
\[
{}y^{\prime \prime }+4 y = 3 t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.040 |
|
|
\[
{}y^{\prime \prime } = 3 t^{4}-2 t
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.148 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+13 y = 2 t \,{\mathrm e}^{-2 t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
15.683 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = -1
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.868 |
|
|
\[
{}5 y^{\prime \prime }+y^{\prime }-4 y = -3
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.898 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 32 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.923 |
|
|
\[
{}16 y^{\prime \prime }-8 y^{\prime }-15 y = 75 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.943 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+26 y = -338 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
9.806 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }-4 y = -32 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.699 |
|
|
\[
{}8 y^{\prime \prime }+6 y^{\prime }+y = 5 t^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.956 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+8 y = -256 t^{3}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.069 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 52 \sin \left (3 t \right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.095 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+13 y = 25 \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.171 |
|
|
\[
{}y^{\prime \prime }-9 y = 54 t \sin \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.477 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = -78 \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.584 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = -32 t^{2} \cos \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.719 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-20 y = -2 \,{\mathrm e}^{t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.562 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-5 y = -648 t^{2} {\mathrm e}^{5 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.109 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = -2 t^{3} {\mathrm e}^{4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.016 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.452 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.572 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.677 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = t^{2}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.652 |
|
|
\[
{}y^{\prime \prime } = t^{2}+{\mathrm e}^{t}+\sin \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.658 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } = 18
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.051 |
|
|
\[
{}y^{\prime \prime }-y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.254 |
|
|
\[
{}y^{\prime \prime }-4 y = 32 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.127 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = -2
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.242 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 3 t
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.676 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = 4
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.281 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = t \,{\mathrm e}^{-t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.243 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+25 y = -1
\] |
[[_2nd_order, _missing_x]] |
✓ |
12.833 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = -{\mathrm e}^{3 t}-2 t
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.092 |
|
|
\[
{}y^{\prime \prime }-y^{\prime } = -3 t -4 t^{2} {\mathrm e}^{2 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.105 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 2 t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.139 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = -24 t -6-4 t \,{\mathrm e}^{-4 t}+{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.200 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } = {\mathrm e}^{-3 t}-{\mathrm e}^{3 t}
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.158 |
|
|
\[
{}y^{\prime \prime }+9 y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 0 & \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.884 |
|
|
\[
{}y^{\prime \prime }+9 \pi ^{2} y = \left \{\begin {array}{cc} 2 t & 0\le t <\pi \\ 2 t -2 \pi & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.691 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} 0 & 0\le t <\pi \\ 10 & \pi \le t <2 \pi \\ 0 & 2 \pi \le t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.786 |
|
|
\[
{}y^{\prime }-4 y = t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.900 |
|
|
\[
{}y^{\prime }+y = \cos \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.366 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.165 |
|
|
\[
{}y^{\prime }+4 y = {\mathrm e}^{-4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.075 |
|
|
\[
{}y^{\prime }+4 y = t \,{\mathrm e}^{-4 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.563 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = f \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.778 |
|
|
\[
{}x^{\prime \prime }+9 x = \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.028 |
|
|
\[
{}4 y^{\prime \prime }+4 y^{\prime }+37 y = \cos \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
9.613 |
|
|
\[
{}y^{\prime \prime }+4 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.108 |
|
|
\[
{}y^{\prime \prime }+16 y^{\prime } = t
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.566 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+10 y = {\mathrm e}^{3 t}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.951 |
|
|
\[
{}y^{\prime \prime }+16 y = 2 \cos \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.967 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+20 y = 2 t \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
20.229 |
|
|
\[
{}y^{\prime \prime }+\frac {y}{4} = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.742 |
|
|
\[
{}y^{\prime \prime }+16 y = \csc \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.733 |
|
|
\[
{}y^{\prime \prime }+16 y = \cot \left (4 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.806 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+50 y = {\mathrm e}^{-t} \csc \left (7 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.086 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+25 y = {\mathrm e}^{-3 t} \left (\sec \left (4 t \right )+\csc \left (4 t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.213 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+26 y = {\mathrm e}^{t} \left (\sec \left (5 t \right )+\csc \left (5 t \right )\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
7.249 |
|
|
\[
{}y^{\prime \prime }+12 y^{\prime }+37 y = {\mathrm e}^{-6 t} \csc \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.292 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+34 y = {\mathrm e}^{3 t} \tan \left (5 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
13.819 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+34 y = {\mathrm e}^{5 t} \cot \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
11.618 |
|
|
\[
{}y^{\prime \prime }-12 y^{\prime }+37 y = {\mathrm e}^{6 t} \sec \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.398 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+17 y = {\mathrm e}^{4 t} \sec \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.381 |
|
|
\[
{}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.538 |
|
|
\[
{}y^{\prime \prime }-25 y = \frac {1}{1-{\mathrm e}^{5 t}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.714 |
|
|
\[
{}y^{\prime \prime }-y = 2 \sinh \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.753 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.013 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = \frac {{\mathrm e}^{2 t}}{t^{2}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.026 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{4}}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.054 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = \frac {{\mathrm e}^{-3 t}}{t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.053 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = {\mathrm e}^{-3 t} \ln \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.077 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left ({\mathrm e}^{t}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.781 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+4 y = {\mathrm e}^{-2 t} \sqrt {-t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.168 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \sqrt {-t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.163 |
|
|
\[
{}y^{\prime \prime }-10 y^{\prime }+25 y = {\mathrm e}^{5 t} \ln \left (2 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.175 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{2 t} \arctan \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.660 |
|
|
\[
{}y^{\prime \prime }+8 y^{\prime }+16 y = \frac {{\mathrm e}^{-4 t}}{t^{2}+1}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.128 |
|
|
\[
{}y^{\prime \prime }+y = \sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
6.428 |
|