|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+g y+\beta z \\ y^{\prime }=g x+b y+\alpha z \\ z^{\prime }=\beta x+\alpha y+c z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
159.971 |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }=2 x-t \\ t^{3} y^{\prime }=-x+t^{2} y+t \\ t^{4} z^{\prime }=-x-t^{2} y+t^{3} z+t \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.086 |
|
|
\[
{}\left [\begin {array}{c} a t x^{\prime }=b c \left (y-z\right ) \\ b t y^{\prime }=c a \left (z-x\right ) \\ c t z^{\prime }=a b \left (x-y\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.075 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=a x_{2}+b x_{3} \cos \left (c t \right )+b x_{4} \sin \left (c t \right ) \\ x_{2}^{\prime }=-a x_{1}+b x_{3} \sin \left (c t \right )-b x_{4} \cos \left (c t \right ) \\ x_{3}^{\prime }=-b x_{1} \cos \left (c t \right )-b x_{2} \sin \left (c t \right )+a x_{4} \\ x_{4}^{\prime }=-b x_{1} \sin \left (c t \right )+b x_{2} \cos \left (c t \right )-a x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.095 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \left (x+y\right ) \\ y^{\prime }=y \left (x+y\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.067 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\left (a y+b \right ) x \\ y^{\prime }=\left (c x+d \right ) y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.056 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (a \left (p x+q y\right )+\alpha \right ) \\ y^{\prime }=y \left (\beta +b \left (p x+q y\right )\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.068 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=h \left (a -x\right ) \left (c -x-y\right ) \\ y^{\prime }=k \left (b -y\right ) \left (c -x-y\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.071 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y^{2}-\cos \left (x\right ) \\ y^{\prime }=-y \sin \left (x\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.065 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \,y^{2}+x+y \\ y^{\prime }=y \,x^{2}-x-y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.064 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-x \left (x^{2}+y^{2}\right ) \\ y^{\prime }=-x+y-y \left (x^{2}+y^{2}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.071 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y+x \left (x^{2}+y^{2}-1\right ) \\ y^{\prime }=x+y \left (x^{2}+y^{2}-1\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.066 |
|
|
\[
{}\left [\begin {array}{c} \left (t^{2}+1\right ) x^{\prime }=-t x+y \\ \left (t^{2}+1\right ) y^{\prime }=-x-t y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.067 |
|
|
\[
{}\left [\begin {array}{c} \left (x^{2}+y^{2}-t^{2}\right ) x^{\prime }=-2 t x \\ \left (x^{2}+y^{2}-t^{2}\right ) y^{\prime }=-2 t y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.076 |
|
|
\[
{}\left [\begin {array}{c} {x^{\prime }}^{2}+t x^{\prime }+a y^{\prime }-x=0 \\ x^{\prime } y^{\prime }+y^{\prime } t -y=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.088 |
|
|
\[
{}\left [\begin {array}{c} x=t x^{\prime }+f \left (x^{\prime }, y^{\prime }\right ) \\ y=y^{\prime } t +g \left (x^{\prime }, y^{\prime }\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.087 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=a \,{\mathrm e}^{2 x}-{\mathrm e}^{-x}+{\mathrm e}^{-2 x} \cos \left (y\right )^{2} \\ y^{\prime \prime }={\mathrm e}^{-2 x} \sin \left (y\right ) \cos \left (y\right )-\frac {\sin \left (y\right )}{\cos \left (y\right )^{3}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.074 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime \prime }=\frac {k x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \\ y^{\prime \prime }=\frac {k y}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.103 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-z \\ y^{\prime }=x^{2}+y \\ z^{\prime }=x^{2}+z \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.064 |
|
|
\[
{}\left [\begin {array}{c} a x^{\prime }=\left (b -c \right ) y z \\ b y^{\prime }=\left (c -a \right ) z x \\ c z^{\prime }=\left (a -b \right ) x y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.068 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (y-z\right ) \\ y^{\prime }=y \left (z-x\right ) \\ z^{\prime }=z \left (x-y\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.062 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }=x y \\ y^{\prime }+z^{\prime }=y z \\ x^{\prime }+z^{\prime }=x z \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.068 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {x^{2}}{2}-\frac {y}{24} \\ y^{\prime }=2 x y-3 z \\ z^{\prime }=3 x z-\frac {y^{2}}{6} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.063 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (y^{2}-z^{2}\right ) \\ y^{\prime }=y \left (z^{2}-x^{2}\right ) \\ z^{\prime }=z \left (x^{2}-y^{2}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.069 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \left (y^{2}-z^{2}\right ) \\ y^{\prime }=-y \left (z^{2}+x^{2}\right ) \\ z^{\prime }=z \left (x^{2}+y^{2}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.065 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \,y^{2}+x+y \\ y^{\prime }=y \,x^{2}-x-y \\ z^{\prime }=y^{2}-x^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.066 |
|
|
\[
{}\left [\begin {array}{c} \left (x-y\right ) \left (x-z\right ) x^{\prime }=f \left (t \right ) \\ \left (y-x\right ) \left (y-z\right ) y^{\prime }=f \left (t \right ) \\ \left (z-x\right ) \left (z-y\right ) z^{\prime }=f \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.076 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime } \sin \left (x_{2}\right )=x_{4} \sin \left (x_{3}\right )+x_{5} \cos \left (x_{3}\right ) \\ x_{2}^{\prime }=x_{4} \cos \left (x_{3}\right )-x_{5} \sin \left (x_{3}\right ) \\ x_{3}^{\prime }+x_{1}^{\prime } \cos \left (x_{2}\right )=a \\ x_{4}^{\prime }-\left (1-\lambda \right ) a x_{5}=-m \sin \left (x_{2}\right ) \cos \left (x_{3}\right ) \\ x_{5}^{\prime }+\left (1-\lambda \right ) a x_{4}=m \sin \left (x_{2}\right ) \sin \left (x_{3}\right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.097 |
|
|
\(\left [\begin {array}{cc} 4 & -2 \\ 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.145 |
|
|
\(\left [\begin {array}{cc} 5 & -6 \\ 3 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.156 |
|
|
\(\left [\begin {array}{cc} 8 & -6 \\ 3 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.147 |
|
|
\(\left [\begin {array}{cc} 4 & -3 \\ 2 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.151 |
|
|
\(\left [\begin {array}{cc} 10 & -9 \\ 6 & -5 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.152 |
|
|
\(\left [\begin {array}{cc} 6 & -4 \\ 3 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.159 |
|
|
\(\left [\begin {array}{cc} 10 & -8 \\ 6 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.148 |
|
|
\(\left [\begin {array}{cc} 7 & -6 \\ 12 & -10 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.153 |
|
|
\(\left [\begin {array}{cc} 8 & -10 \\ 2 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.151 |
|
|
\(\left [\begin {array}{cc} 9 & -10 \\ 2 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.155 |
|
|
\(\left [\begin {array}{cc} 19 & -10 \\ 21 & -10 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.155 |
|
|
\(\left [\begin {array}{cc} 13 & -15 \\ 6 & -6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.152 |
|
|
\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ 2 & -2 & -1 \\ -2 & 6 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.258 |
|
|
\(\left [\begin {array}{ccc} 5 & 0 & 0 \\ 4 & -4 & -2 \\ -2 & 12 & 6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.255 |
|
|
\(\left [\begin {array}{ccc} 2 & -2 & 0 \\ 2 & -2 & -1 \\ -2 & 2 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.240 |
|
|
\(\left [\begin {array}{ccc} 1 & 0 & -1 \\ -2 & 3 & -1 \\ -6 & 6 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.246 |
|
|
\(\left [\begin {array}{ccc} 3 & 5 & -2 \\ 0 & 2 & 0 \\ 0 & 2 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.230 |
|
|
\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -6 & 8 & 2 \\ 12 & -15 & -3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.275 |
|
|
\(\left [\begin {array}{ccc} 3 & 6 & -2 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.187 |
|
|
\(\left [\begin {array}{ccc} 1 & 0 & 0 \\ -4 & 7 & 2 \\ 10 & -15 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.217 |
|
|
\(\left [\begin {array}{ccc} 4 & -3 & 1 \\ 2 & -1 & 1 \\ 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.189 |
|
|
\(\left [\begin {array}{ccc} 5 & -6 & 3 \\ 6 & -7 & 3 \\ 6 & -6 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.216 |
|
|
\(\left [\begin {array}{cccc} 1 & 2 & 2 & 2 \\ 0 & 2 & 2 & 2 \\ 0 & 0 & 3 & 2 \\ 0 & 0 & 0 & 4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.319 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & 4 & 0 \\ 0 & 1 & 4 & 0 \\ 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.251 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.221 |
|
|
\(\left [\begin {array}{cccc} 4 & 0 & 0 & -3 \\ 0 & 2 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 6 & 0 & 0 & -5 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.330 |
|
|
\(\left [\begin {array}{cc} 0 & 1 \\ -1 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.174 |
|
|
\(\left [\begin {array}{cc} 0 & -6 \\ 6 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.188 |
|
|
\(\left [\begin {array}{cc} 0 & -3 \\ 12 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.189 |
|
|
\(\left [\begin {array}{cc} 0 & -12 \\ 12 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.187 |
|
|
\(\left [\begin {array}{cc} 0 & 24 \\ -6 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.185 |
|
|
\(\left [\begin {array}{cc} 0 & -4 \\ 36 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.193 |
|
|
\(\left [\begin {array}{ccc} 32 & -67 & 47 \\ 7 & -14 & 13 \\ -7 & 15 & -6 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.266 |
|
|
\(\left [\begin {array}{cccc} 22 & -9 & -8 & -8 \\ 10 & -7 & -14 & 2 \\ 10 & 0 & 8 & -10 \\ 29 & -9 & -3 & -15 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.514 |
|
|
\(\left [\begin {array}{cc} 5 & -4 \\ 2 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.154 |
|
|
\(\left [\begin {array}{cc} 6 & -6 \\ 4 & -4 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.149 |
|
|
\(\left [\begin {array}{cc} 5 & -3 \\ 2 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.151 |
|
|
\(\left [\begin {array}{cc} 5 & -4 \\ 3 & -2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.153 |
|
|
\(\left [\begin {array}{cc} 9 & -8 \\ 6 & -5 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.157 |
|
|
\(\left [\begin {array}{cc} 10 & -6 \\ 12 & -7 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.155 |
|
|
\(\left [\begin {array}{cc} 6 & -10 \\ 2 & -3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.152 |
|
|
\(\left [\begin {array}{cc} 11 & -15 \\ 6 & -8 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.154 |
|
|
\(\left [\begin {array}{cc} -1 & 4 \\ -1 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.114 |
|
|
\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\) |
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 |
✓ |
0.110 |
|
|
\(\left [\begin {array}{ccc} 1 & 3 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.180 |
|
|
\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ 2 & -2 & 1 \\ 2 & -2 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.202 |
|
|
\(\left [\begin {array}{ccc} 3 & -3 & 1 \\ 2 & -2 & 1 \\ 0 & 0 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.187 |
|
|
\(\left [\begin {array}{ccc} 3 & -2 & 0 \\ 0 & 1 & 0 \\ -4 & 4 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.201 |
|
|
\(\left [\begin {array}{ccc} 7 & -8 & 3 \\ 6 & -7 & 3 \\ 2 & -2 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.273 |
|
|
\(\left [\begin {array}{ccc} 6 & -5 & 2 \\ 4 & -3 & 2 \\ 2 & -2 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.253 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ -2 & 4 & -1 \\ -4 & 4 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.247 |
|
|
\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ -6 & 11 & 2 \\ 6 & -15 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.277 |
|
|
\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ -1 & 2 & 0 \\ -1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.132 |
|
|
\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ -1 & 2 & 0 \\ -5 & 7 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.128 |
|
|
\(\left [\begin {array}{ccc} -2 & 4 & -1 \\ -3 & 5 & -1 \\ -1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.194 |
|
|
\(\left [\begin {array}{ccc} 3 & -2 & 1 \\ 1 & 0 & 1 \\ -1 & 1 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.183 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & -2 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.209 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.202 |
|
|
\(\left [\begin {array}{cccc} 1 & 1 & 0 & 0 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.196 |
|
|
\(\left [\begin {array}{cccc} 1 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
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 |
✓ |
0.160 |
|
|
\[
{}y^{\prime } = f \left (x \right )
\] |
[_quadrature] |
✓ |
0.431 |
|
|
\[
{}y^{\prime } = f \left (y\right )
\] |
[_quadrature] |
✓ |
0.590 |
|
|
\[
{}y^{\prime } = f \left (x \right ) g \left (y\right )
\] |
[_separable] |
✓ |
1.009 |
|
|
\[
{}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{0} \left (x \right )
\] |
[_linear] |
✓ |
1.747 |
|
|
\[
{}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n}
\] |
[_Bernoulli] |
✓ |
2.415 |
|
|
\[
{}y^{\prime } = f \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.419 |
|
|
\[
{}y^{\prime } = a y^{2}+b x +c
\] |
[_Riccati] |
✓ |
1.253 |
|
|
\[
{}y^{\prime } = y^{2}-a^{2} x^{2}+3 a
\] |
[_Riccati] |
✓ |
1.760 |
|
|
\[
{}y^{\prime } = y^{2}+a^{2} x^{2}+b x +c
\] |
[_Riccati] |
✓ |
9.463 |
|