|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.156 |
|
|
\[
{}\left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.112 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.639 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.623 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+\frac {8}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.631 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (2 x^{2}+\frac {5}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.635 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.613 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.652 |
|
|
\[
{}3 x y^{\prime \prime }-\left (-2+x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.683 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.577 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.653 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{4}+x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.622 |
|
|
\[
{}x y^{\prime \prime }-\left (x^{2}+2\right ) y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
0.608 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.710 |
|
|
\[
{}\left (2 x^{2}-x \right ) y^{\prime \prime }+\left (2 x -2\right ) y^{\prime }+\left (-2 x^{2}+3 x -2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.739 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\frac {3 y}{4} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.613 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.250 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.286 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+8 \left (x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.293 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-\frac {3 y}{4} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.390 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.505 |
|
|
\[
{}2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.203 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.507 |
|
|
\[
{}x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}-3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.235 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-2 x-4 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-y={\mathrm e}^{4 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.277 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=-2 t \\ x^{\prime }+y^{\prime }-3 x-y=t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.175 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+x={\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.176 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-2 y=2 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-3 x-4 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.103 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y={\mathrm e}^{-t} \\ x^{\prime }+2 x+y^{\prime }+y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.767 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-3 x-y=t \\ x^{\prime }+y^{\prime }-4 x-y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.476 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-6 y={\mathrm e}^{3 t} \\ x^{\prime }+2 y^{\prime }-2 x-6 y=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.713 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y=3 t \\ x^{\prime }+2 y^{\prime }-2 x-3 y=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.710 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }+2 y=\sin \left (t \right ) \\ x^{\prime }+y^{\prime }-x-y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.305 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y^{\prime }-2 x+4 y=t \\ x^{\prime }+y^{\prime }-x-y=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.486 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+5 y=4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.459 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x+5 y=t^{2} \\ x^{\prime }+2 y^{\prime }-2 x+4 y=2 t +1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.559 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+y=t^{2}+4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 t^{2}-2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.479 |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+2 y^{\prime }-x+y=t -1 \\ x^{\prime }+y^{\prime }-x=t +2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.718 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+4 y^{\prime }+x-y=3 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+2 x+2 y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.520 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=-2 t \\ x^{\prime }+y^{\prime }+x-y=t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.467 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=1 \\ x^{\prime }+y^{\prime }+2 x-y=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.468 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.567 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+3 y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.585 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+2 y+5 t \\ y^{\prime }=3 x+4 y+17 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.504 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.439 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.447 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+7 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.604 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=7 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.605 |
|
|
\(\left [\begin {array}{cc} 1 & 2 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.116 |
|
|
\(\left [\begin {array}{cc} 3 & 2 \\ 6 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.119 |
|
|
\(\left [\begin {array}{cc} 3 & 1 \\ 12 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.122 |
|
|
\(\left [\begin {array}{cc} -2 & 7 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.131 |
|
|
\(\left [\begin {array}{cc} 3 & 4 \\ 5 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.117 |
|
|
\(\left [\begin {array}{cc} 3 & -5 \\ -4 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.132 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.275 |
|
|
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.287 |
|
|
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.268 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.256 |
|
|
\(\left [\begin {array}{ccc} 1 & 3 & -6 \\ 0 & 2 & 2 \\ 0 & -1 & 5 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.256 |
|
|
\(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.284 |
|
|
\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.283 |
|
|
\(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.284 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=2 x+3 y-4 z \\ z^{\prime }=4 x+y-4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.533 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y-z \\ y^{\prime }=x+3 y+z \\ z^{\prime }=-3 x-6 y+6 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.501 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.479 |
|
|
\[
{}y^{\prime }+y = 2 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.485 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.200 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.299 |
|
|
\[
{}y^{\prime \prime }+4 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.355 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.374 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 18 \,{\mathrm e}^{-t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.507 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = t \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.338 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 4 t \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.333 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+15 y = 9 t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.328 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 20 \sin \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.440 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 36 t \,{\mathrm e}^{4 t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.399 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.920 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.089 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.651 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.859 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.156 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.753 |
|
|
\[
{}t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.253 |
|
|
\[
{}t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.114 |
|
|
\[
{}\left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.436 |
|
|
\[
{}t^{3} x^{\prime \prime \prime }-\left (3+t \right ) t^{2} x^{\prime \prime }+2 t \left (3+t \right ) x^{\prime }-2 \left (3+t \right ) x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.042 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.262 |
|
|
\[
{}\left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.007 |
|
|
\[
{}t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.182 |
|
|
\[
{}t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.260 |
|
|
\[
{}t^{3} x^{\prime \prime }+3 t^{2} x^{\prime }+x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.745 |
|
|
\[
{}\sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.853 |
|
|
\[
{}\frac {\left (t +1\right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.013 |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime }+x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.145 |
|
|
\[
{}\left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.974 |
|
|
\[
{}x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x = 0
\] |
[_Lienard] |
✗ |
1.252 |
|
|
\[
{}f \left (t \right ) x^{\prime \prime }+x g \left (t \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.433 |
|
|
\[
{}x^{\prime \prime }+\left (t +1\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.418 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.071 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.020 |
|