|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x=x^{\prime } t +f \left (x^{\prime }, y^{\prime }\right ) \\ y=t y^{\prime }+g \left (x^{\prime }, y^{\prime }\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.071 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=a \,{\mathrm e}^{2 x}-{\mathrm e}^{-x}+{\mathrm e}^{-2 x} \cos \left (y\right )^{2} \\ y^{\prime \prime }={\mathrm e}^{-2 x} \sin \left (y\right ) \cos \left (y\right )-\frac {\sin \left (y\right )}{\cos \left (y\right )^{3}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.055 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=\frac {k x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \\ y^{\prime \prime }=\frac {k y}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.049 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-z \\ y^{\prime }=x^{2}+y \\ z^{\prime }=x^{2}+z \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.053 |
|
|
\[
{}\left [\begin {array}{c} a x^{\prime }=\left (b -c \right ) y z \\ b y^{\prime }=\left (c -a \right ) z x \\ c z^{\prime }=\left (a -b \right ) x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (y-z\right ) \\ y^{\prime }=y \left (z-x\right ) \\ z^{\prime }=z \left (x-y\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }=x y \\ y^{\prime }+z^{\prime }=y z \\ x^{\prime }+z^{\prime }=x z \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {x^{2}}{2}-\frac {y}{24} \\ y^{\prime }=2 x y-3 z \\ z^{\prime }=3 x z-\frac {y^{2}}{6} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (y^{2}-z^{2}\right ) \\ y^{\prime }=y \left (z^{2}-x^{2}\right ) \\ z^{\prime }=z \left (x^{2}-y^{2}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (y^{2}-z^{2}\right ) \\ y^{\prime }=-y \left (z^{2}+x^{2}\right ) \\ z^{\prime }=z \left (x^{2}+y^{2}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \,y^{2}+x+y \\ y^{\prime }=y \,x^{2}-x-y \\ z^{\prime }=y^{2}-x^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.058 |
|
|
\[
{}\left [\begin {array}{c} \left (x-y\right ) \left (x-z\right ) x^{\prime }=f \left (t \right ) \\ \left (y-x\right ) \left (y-z\right ) y^{\prime }=f \left (t \right ) \\ \left (z-x\right ) \left (z-y\right ) z^{\prime }=f \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.063 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime } \sin \left (x_{2}\right )=x_{4} \sin \left (x_{3}\right )+x_{5} \cos \left (x_{3}\right ) \\ x_{2}^{\prime }=x_{4} \cos \left (x_{3}\right )-x_{5} \sin \left (x_{3}\right ) \\ x_{3}^{\prime }+x_{1}^{\prime } \cos \left (x_{2}\right )=a \\ x_{4}^{\prime }-\left (1-\lambda \right ) a x_{5}=-m \sin \left (x_{2}\right ) \cos \left (x_{3}\right ) \\ x_{5}^{\prime }+\left (1-\lambda \right ) a x_{4}=m \sin \left (x_{2}\right ) \sin \left (x_{3}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.076 |
|
|
\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.141 |
|
|
\(\left [\begin {array}{cc} 5 & -6 \\ 3 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.145 |
|
|
\(\left [\begin {array}{cc} 8 & -6 \\ 3 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.143 |
|
|
\(\left [\begin {array}{cc} 4 & -3 \\ 2 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.147 |
|
|
\(\left [\begin {array}{cc} 10 & -9 \\ 6 & -5 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.148 |
|
|
\(\left [\begin {array}{cc} 6 & -4 \\ 3 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.147 |
|
|
\(\left [\begin {array}{cc} 10 & -8 \\ 6 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.151 |
|
|
\(\left [\begin {array}{cc} 7 & -6 \\ 12 & -10 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.157 |
|
|
\(\left [\begin {array}{cc} 8 & -10 \\ 2 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.148 |
|
|
\(\left [\begin {array}{cc} 9 & -10 \\ 2 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.152 |
|
|
\(\left [\begin {array}{cc} 19 & -10 \\ 21 & -10 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.155 |
|
|
\(\left [\begin {array}{cc} 13 & -15 \\ 6 & -6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.158 |
|
|
\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ 2 & -2 & -1 \\ -2 & 6 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.253 |
|
|
\(\left [\begin {array}{ccc} 5 & 0 & 0 \\ 4 & -4 & -2 \\ -2 & 12 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.269 |
|
|
\(\left [\begin {array}{ccc} 2 & -2 & 0 \\ 2 & -2 & -1 \\ -2 & 2 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.255 |
|
|
\(\left [\begin {array}{ccc} 1 & 0 & -1 \\ -2 & 3 & -1 \\ -6 & 6 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.292 |
|
|
\(\left [\begin {array}{ccc} 3 & 5 & -2 \\ 0 & 2 & 0 \\ 0 & 2 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.233 |
|
|
\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -6 & 8 & 2 \\ 12 & -15 & -3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.271 |
|
|
\(\left [\begin {array}{ccc} 3 & 6 & -2 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.185 |
|
|
\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -4 & 7 & 2 \\ 10 & -15 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.208 |
|
|
\(\left [\begin {array}{ccc} 4 & -3 & 1 \\ 2 & -1 & 1 \\ 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.194 |
|
|
\(\left [\begin {array}{ccc} 5 & -6 & 3 \\ 6 & -7 & 3 \\ 6 & -6 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.198 |
|
|
\(\left [\begin {array}{cccc} 1 & 2 & 2 & 2 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 3 & 2 \\ 0 & 0 & 0 & 4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.334 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & 4 & 0 \\ 0 & 1 & 4 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.221 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.208 |
|
|
\(\left [\begin {array}{cccc} 4 & 0 & 0 & -3 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 6 & 0 & 0 & -5 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.335 |
|
|
\(\left [\begin {array}{cc} 0 & 1 \\ -1 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.167 |
|
|
\(\left [\begin {array}{cc} 0 & -6 \\ 6 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.178 |
|
|
\(\left [\begin {array}{cc} 0 & -3 \\ 12 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.192 |
|
|
\(\left [\begin {array}{cc} 0 & -12 \\ 12 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.179 |
|
|
\(\left [\begin {array}{cc} 0 & 24 \\ -6 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.188 |
|
|
\(\left [\begin {array}{cc} 0 & -4 \\ 36 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.187 |
|
|
\(\left [\begin {array}{ccc} 32 & -67 & 47 \\ 7 & -14 & 13 \\ -7 & 15 & -6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.264 |
|
|
\(\left [\begin {array}{cccc} 22 & -9 & -8 & -8 \\ 10 & -7 & -14 & 2 \\ 10 & 0 & 8 & -10 \\ 29 & -9 & -3 & -15 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.529 |
|
|
\(\left [\begin {array}{cc} 5 & -4 \\ 2 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.151 |
|
|
\(\left [\begin {array}{cc} 6 & -6 \\ 4 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.146 |
|
|
\(\left [\begin {array}{cc} 5 & -3 \\ 2 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.152 |
|
|
\(\left [\begin {array}{cc} 5 & -4 \\ 3 & -2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.148 |
|
|
\(\left [\begin {array}{cc} 9 & -8 \\ 6 & -5 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.148 |
|
|
\(\left [\begin {array}{cc} 10 & -6 \\ 12 & -7 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.151 |
|
|
\(\left [\begin {array}{cc} 6 & -10 \\ 2 & -3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.152 |
|
|
\(\left [\begin {array}{cc} 11 & -15 \\ 6 & -8 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.156 |
|
|
\(\left [\begin {array}{cc} -1 & 4 \\ -1 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.108 |
|
|
\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.104 |
|
|
\(\left [\begin {array}{cc} 5 & 1 \\ -9 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.112 |
|
|
\(\left [\begin {array}{cc} 11 & 9 \\ -16 & -13 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.112 |
|
|
\(\left [\begin {array}{ccc} 1 & 3 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.171 |
|
|
\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ 2 & -2 & 1 \\ 2 & -2 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.189 |
|
|
\(\left [\begin {array}{ccc} 3 & -3 & 1 \\ 2 & -2 & 1 \\ 0 & 0 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.192 |
|
|
\(\left [\begin {array}{ccc} 3 & -2 & 0 \\ 0 & 1 & 0 \\ -4 & 4 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.188 |
|
|
\(\left [\begin {array}{ccc} 7 & -8 & 3 \\ 6 & -7 & 3 \\ 2 & -2 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.264 |
|
|
\(\left [\begin {array}{ccc} 6 & -5 & 2 \\ 4 & -3 & 2 \\ 2 & -2 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.261 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ -2 & 4 & -1 \\ -4 & 4 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.257 |
|
|
\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ -6 & 11 & 2 \\ 6 & -15 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.263 |
|
|
\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ -1 & 2 & 0 \\ -1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.135 |
|
|
\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ -1 & 2 & 0 \\ -5 & 7 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.132 |
|
|
\(\left [\begin {array}{ccc} -2 & 4 & -1 \\ -3 & 5 & -1 \\ -1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.188 |
|
|
\(\left [\begin {array}{ccc} 3 & -2 & 1 \\ 1 & 0 & 1 \\ -1 & 1 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.193 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & -2 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.220 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.215 |
|
|
\(\left [\begin {array}{cccc} 1 & 1 & 0 & 0 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.182 |
|
|
\(\left [\begin {array}{cccc} 1 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.180 |
|
|
\(\left [\begin {array}{ccccc} 2 & 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.149 |
|
|
\[
{}y^{\prime } = f \left (x \right )
\] |
[_quadrature] |
✓ |
0.466 |
|
|
\[
{}y^{\prime } = f \left (y\right )
\] |
[_quadrature] |
✓ |
0.670 |
|
|
\[
{}y^{\prime } = f \left (x \right ) g \left (y\right )
\] |
[_separable] |
✓ |
1.036 |
|
|
\[
{}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{0} \left (x \right )
\] |
[_linear] |
✓ |
2.166 |
|
|
\[
{}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n}
\] |
[_Bernoulli] |
✓ |
2.619 |
|
|
\[
{}y^{\prime } = f \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.294 |
|
|
\[
{}y^{\prime } = y^{2} a +b x +c
\] |
[_Riccati] |
✓ |
1.354 |
|
|
\[
{}y^{\prime } = y^{2}-a^{2} x^{2}+3 a
\] |
[_Riccati] |
✓ |
1.904 |
|
|
\[
{}y^{\prime } = y^{2}+a^{2} x^{2}+b x +c
\] |
[_Riccati] |
✓ |
8.704 |
|
|
\[
{}y^{\prime } = y^{2} a +b \,x^{n}
\] |
[[_Riccati, _special]] |
✓ |
1.632 |
|
|
\[
{}y^{\prime } = y^{2}+a n \,x^{n -1}-a^{2} x^{2 n}
\] |
[_Riccati] |
✗ |
595.205 |
|
|
\[
{}y^{\prime } = y^{2} a +b \,x^{2 n}+c \,x^{n -1}
\] |
[_Riccati] |
✓ |
3.506 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{-n -2}
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
2.635 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m}
\] |
[_Riccati] |
✓ |
2.177 |
|
|
\[
{}y^{\prime } = y^{2}+k \left (a x +b \right )^{n} \left (c x +d \right )^{-n -4}
\] |
[_Riccati] |
✗ |
7.766 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m}
\] |
[_Riccati] |
✗ |
410.809 |
|
|
\[
{}y^{\prime } = \left (a \,x^{2 n}+b \,x^{n -1}\right ) y^{2}+c
\] |
[_Riccati] |
✓ |
50.787 |
|
|
\[
{}\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} x +b_{0} = 0
\] |
[_rational, _Riccati] |
✓ |
3.579 |
|
|
\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
1.976 |
|
|
\[
{}x^{2} y^{\prime } = x^{2} y^{2}-a^{2} x^{4}+a \left (-2 b +1\right ) x^{2}-b \left (b +1\right )
\] |
[_rational, _Riccati] |
✓ |
2.595 |
|
|
\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b \,x^{n}+c
\] |
[_rational, _Riccati] |
✓ |
2.344 |
|
|
\[
{}x^{2} y^{\prime } = x^{2} y^{2}+a \,x^{2 m} \left (b \,x^{m}+c \right )^{n}-\frac {n^{2}}{4}+\frac {1}{4}
\] |
[_Riccati] |
✗ |
4.306 |
|
|
\[
{}\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} = 0
\] |
[_rational, _Riccati] |
✓ |
8.400 |
|
|
\[
{}x^{4} y^{\prime } = -x^{4} y^{2}-a^{2}
\] |
[_rational, [_Riccati, _special]] |
✓ |
3.170 |
|