|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.140 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.711 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (x^{2}-3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.133 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-2 x-4 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-y={\mathrm e}^{4 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.219 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x=-2 t \\ x^{\prime }+y^{\prime }-3 x-y=t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.183 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y={\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+x={\mathrm e}^{3 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.173 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-2 y=2 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }-3 x-4 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.109 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y={\mathrm e}^{-t} \\ x^{\prime }+2 x+y^{\prime }+y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.655 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-3 x-y=t \\ x^{\prime }+y^{\prime }-4 x-y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.472 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-6 y={\mathrm e}^{3 t} \\ x^{\prime }+2 y^{\prime }-2 x-6 y=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.633 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x-3 y=3 t \\ x^{\prime }+2 y^{\prime }-2 x-3 y=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.622 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }+2 y=\sin \left (t \right ) \\ x^{\prime }+y^{\prime }-x-y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.230 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }-y^{\prime }-2 x+4 y=t \\ x^{\prime }+y^{\prime }-x-y=1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.485 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+5 y=4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.460 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-x+5 y=t^{2} \\ x^{\prime }+2 y^{\prime }-2 x+4 y=2 t +1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.388 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }+x+y=t^{2}+4 t \\ x^{\prime }+y^{\prime }+2 x+2 y=2 t^{2}-2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.480 |
|
|
\[
{}\left [\begin {array}{c} 3 x^{\prime }+2 y^{\prime }-x+y=t -1 \\ x^{\prime }+y^{\prime }-x=t +2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.611 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+4 y^{\prime }+x-y=3 \,{\mathrm e}^{t} \\ x^{\prime }+y^{\prime }+2 x+2 y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.499 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=-2 t \\ x^{\prime }+y^{\prime }+x-y=t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.472 |
|
|
\[
{}\left [\begin {array}{c} 2 x^{\prime }+y^{\prime }-x-y=1 \\ x^{\prime }+y^{\prime }+2 x-y=t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.460 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=2 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+3 y \\ y^{\prime }=4 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.541 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+2 y+5 t \\ y^{\prime }=3 x+4 y+17 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.499 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.398 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.408 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+7 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.572 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=7 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.607 |
|
|
\(\left [\begin {array}{cc} 1 & 2 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.144 |
|
|
\(\left [\begin {array}{cc} 3 & 2 \\ 6 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.149 |
|
|
\(\left [\begin {array}{cc} 3 & 1 \\ 12 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.150 |
|
|
\(\left [\begin {array}{cc} -2 & 7 \\ 3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.148 |
|
|
\(\left [\begin {array}{cc} 3 & 4 \\ 5 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.150 |
|
|
\(\left [\begin {array}{cc} 3 & -5 \\ -4 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.141 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ 2 & 3 & -4 \\ 4 & 1 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.241 |
|
|
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & -6 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.248 |
|
|
\(\left [\begin {array}{ccc} 1 & -1 & -1 \\ 1 & 3 & 1 \\ -3 & 1 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.231 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.218 |
|
|
\(\left [\begin {array}{ccc} 1 & 3 & -6 \\ 0 & 2 & 2 \\ 0 & -1 & 5 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.218 |
|
|
\(\left [\begin {array}{ccc} -5 & -12 & 6 \\ 1 & 5 & -1 \\ -7 & -10 & 8 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.245 |
|
|
\(\left [\begin {array}{ccc} -2 & 5 & 5 \\ -1 & 4 & 5 \\ 3 & -3 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.243 |
|
|
\(\left [\begin {array}{ccc} -2 & 6 & -18 \\ 12 & -23 & 66 \\ 5 & -10 & 29 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.241 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=2 x+3 y-4 z \\ z^{\prime }=4 x+y-4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.508 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y-z \\ y^{\prime }=x+3 y+z \\ z^{\prime }=-3 x-6 y+6 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.493 |
|
|
\[
{}y^{\prime }-y = {\mathrm e}^{3 t}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.422 |
|
|
\[
{}y^{\prime }+y = 2 \sin \left (t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.447 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.217 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.257 |
|
|
\[
{}y^{\prime \prime }+4 y = 8
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.299 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.303 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 18 \,{\mathrm e}^{-t} \sin \left (3 t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.419 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = t \,{\mathrm e}^{-2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.273 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 4 t \,{\mathrm e}^{-3 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.258 |
|
|
\[
{}y^{\prime \prime }-8 y^{\prime }+15 y = 9 t \,{\mathrm e}^{2 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.283 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 20 \sin \left (t \right )
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.367 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 36 t \,{\mathrm e}^{4 t}
\] |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
0.324 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = \left \{\begin {array}{cc} 2 & 0<t <4 \\ 0 & 4<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.537 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = \left \{\begin {array}{cc} 6 & 0<t <2 \\ 0 & 2<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.612 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \left \{\begin {array}{cc} 1 & 0<t <\frac {\pi }{2} \\ 0 & \frac {\pi }{2}<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.565 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = \left \{\begin {array}{cc} 3 & 0<t <2 \pi \\ 0 & 2 \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.313 |
|
|
\[
{}y^{\prime \prime }+4 y = \left \{\begin {array}{cc} -4 t +8 \pi & 0<t <2 \pi \\ 0 & 2<t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.766 |
|
|
\[
{}y^{\prime \prime }+y = \left \{\begin {array}{cc} t & 0<t <\pi \\ \pi & \pi <t \end {array}\right .
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.563 |
|
|
\[
{}t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.315 |
|
|
\[
{}t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.123 |
|
|
\[
{}\left (t^{3}-2 t^{2}\right ) x^{\prime \prime }-\left (t^{3}+2 t^{2}-6 t \right ) x^{\prime }+\left (3 t^{2}-6\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.416 |
|
|
\[
{}t^{3} x^{\prime \prime \prime }-\left (t +3\right ) t^{2} x^{\prime \prime }+2 t \left (t +3\right ) x^{\prime }-2 \left (t +3\right ) x = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.066 |
|
|
\[
{}t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.421 |
|
|
\[
{}\left (2 t +1\right ) x^{\prime \prime }+t^{3} x^{\prime }+x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.795 |
|
|
\[
{}t^{2} x^{\prime \prime }+\left (2 t^{3}+7 t \right ) x^{\prime }+\left (8 t^{2}+8\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.299 |
|
|
\[
{}t^{3} x^{\prime \prime }-\left (t^{3}+2 t^{2}-t \right ) x^{\prime }+\left (t^{2}+t -1\right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.448 |
|
|
\[
{}t^{3} x^{\prime \prime }+3 t^{2} x^{\prime }+x = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.924 |
|
|
\[
{}\sin \left (t \right ) x^{\prime \prime }+\cos \left (t \right ) x^{\prime }+2 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.661 |
|
|
\[
{}\frac {\left (1+t \right ) x^{\prime \prime }}{t}-\frac {x^{\prime }}{t^{2}}+\frac {x}{t^{3}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.162 |
|
|
\[
{}t^{2} x^{\prime \prime }+t x^{\prime }+x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.240 |
|
|
\[
{}\left (t^{4}+t^{2}\right ) x^{\prime \prime }+2 t^{3} x^{\prime }+3 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.969 |
|
|
\[
{}x^{\prime \prime }-\tan \left (t \right ) x^{\prime }+x = 0
\] |
[_Lienard] |
✗ |
1.200 |
|
|
\[
{}f \left (t \right ) x^{\prime \prime }+x g \left (t \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.283 |
|
|
\[
{}x^{\prime \prime }+\left (1+t \right ) x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.563 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.930 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.943 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.919 |
|
|
\[
{}y^{\prime \prime }+\lambda y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.023 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+\frac {\lambda y}{x} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.735 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+\frac {\lambda y}{x} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.705 |
|
|
\[
{}2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.954 |
|
|
\[
{}-\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.457 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.397 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.414 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.424 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-4 y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.455 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.497 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.588 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+7 y \\ y^{\prime }=3 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.416 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.410 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+b y \\ y^{\prime }=c x+d y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.677 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-4 y-x \left (x^{2}+y^{2}\right ) \\ y^{\prime }=4 x+4 y-y \left (x^{2}+y^{2}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.059 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y+\frac {x \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \\ y^{\prime }=-x+\frac {y \left (1-x^{2}-y^{2}\right )}{\sqrt {x^{2}+y^{2}}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.090 |
|
|
\[
{}x^{\prime \prime }+x^{4} x^{\prime }-x^{\prime }+x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
2.562 |
|
|
\[
{}x^{\prime \prime }+x^{\prime }+{x^{\prime }}^{3}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.589 |
|
|
\[
{}x^{\prime \prime }+\left (x^{4}+x^{2}\right ) x^{\prime }+x^{3}+x = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
4.376 |
|