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# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=\frac {x_{1}^{2}}{x_{2}} \\ x_{2}^{\prime }=x_{2}-x_{1} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.129 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\frac {{\mathrm e}^{-x}}{t} \\ y^{\prime }=\frac {x \,{\mathrm e}^{-y}}{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.267 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\frac {t +y}{x+y} \\ y^{\prime }=\frac {x-t}{x+y} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.262 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\frac {t -y}{-x+y} \\ y^{\prime }=\frac {x-t}{-x+y} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.257 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\frac {t +y}{x+y} \\ y^{\prime }=\frac {t +x}{x+y} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.237 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-9 y \\ y^{\prime }=x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.349 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=t +y \\ y^{\prime }=x-t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.595 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }+3 x+4 y=0 \\ y^{\prime }+2 x+5 y=0 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.286 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+5 y \\ y^{\prime }=-x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.332 |
|
|
\[ {}\left [\begin {array}{c} 4 x^{\prime }-y^{\prime }+3 x=\sin \left (t \right ) \\ x^{\prime }+y=\cos \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.878 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-y+z \\ y^{\prime }=z \\ z^{\prime }=-x+z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.589 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y+z \\ y^{\prime }=z+x \\ z^{\prime }=x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.402 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }=y \\ y^{\prime \prime }=x \end {array}\right ] \] |
unknown |
system of linear ODEs |
✗ |
N/A |
|
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }+y^{\prime }+x=0 \\ x^{\prime }+y^{\prime \prime }=0 \end {array}\right ] \] |
unknown |
system of linear ODEs |
✗ |
N/A |
|
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }=3 x+y \\ y^{\prime }=-2 x \end {array}\right ] \] |
unknown |
system of linear ODEs |
✗ |
N/A |
|
|
|
\[ {}\left [\begin {array}{c} x^{\prime \prime }=x^{2}+y \\ y^{\prime }=-2 x x^{\prime }+x \end {array}\right ] \] |
unknown |
system of linear ODEs |
✗ |
N/A |
|
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x^{2}+y^{2} \\ y^{\prime }=2 x y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.244 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-\frac {1}{y} \\ y^{\prime }=\frac {1}{x} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.251 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\frac {x}{y} \\ y^{\prime }=\frac {y}{x} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.242 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\frac {y}{x-y} \\ y^{\prime }=\frac {x}{x-y} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.267 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\sin \left (x\right ) \cos \left (y\right ) \\ y^{\prime }=\cos \left (x\right ) \sin \left (y\right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.266 |
|
|
\[ {}\left [\begin {array}{c} {\mathrm e}^{t} x^{\prime }=\frac {1}{y} \\ {\mathrm e}^{t} y^{\prime }=\frac {1}{x} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.269 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\cos \left (x\right )^{2} \cos \left (y\right )^{2}+\sin \left (x\right )^{2} \cos \left (y\right )^{2} \\ y^{\prime }=-\frac {\sin \left (2 x\right ) \sin \left (2 y\right )}{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
❇ |
N/A |
0.259 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=8 y-x \\ y^{\prime }=x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.293 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=-x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.247 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.373 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x+4 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.274 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-5 y \\ y^{\prime }=x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.301 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y+z-x \\ y^{\prime }=x-y+z \\ z^{\prime }=x+y-z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.412 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-y+z \\ y^{\prime }=x+2 y-z \\ z^{\prime }=x-y+2 z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.385 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-y+z \\ y^{\prime }=z+x \\ z^{\prime }=y-2 z-3 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.353 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }+2 x-y=-{\mathrm e}^{2 t} \\ y^{\prime }+3 x-2 y=6 \,{\mathrm e}^{2 t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.626 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y-\cos \left (t \right ) \\ y^{\prime }=-y-2 x+\cos \left (t \right )+\sin \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.777 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y+\tan \left (t \right )^{2}-1 \\ y^{\prime }=\tan \left (t \right )-x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.716 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x-2 y+\frac {2}{{\mathrm e}^{t}-1} \\ y^{\prime }=6 x+3 y-\frac {3}{{\mathrm e}^{t}-1} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.033 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\frac {1}{\cos \left (t \right )} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.616 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+1 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.65 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3-2 y \\ y^{\prime }=2 x-2 t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.899 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-y+\sin \left (t \right ) \\ y^{\prime }=x+\cos \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.75 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y+{\mathrm e}^{t} \\ y^{\prime }=x+y-{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.556 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-5 y+4 t -1 \\ y^{\prime }=x-2 y+t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.471 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y-x+{\mathrm e}^{t} \\ y^{\prime }=x-y+{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.476 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }+y=t^{2} \\ y^{\prime }-x=t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.76 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }+y^{\prime }+y={\mathrm e}^{-t} \\ 2 x^{\prime }+y^{\prime }+2 y=\sin \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.443 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y-2 z+2-t \\ y^{\prime }=-x+1 \\ z^{\prime }=x+y-z+1-t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.952 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }+x+2 y=2 \,{\mathrm e}^{-t} \\ y^{\prime }+y+z=1 \\ z^{\prime }+z=1 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.564 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=x+2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.283 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=6 x+y \\ y^{\prime }=4 x+3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.282 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-4 y+1 \\ y^{\prime }=-x+5 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.615 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x+y+{\mathrm e}^{t} \\ y^{\prime }=x+3 y-{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.546 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+4 y+\cos \left (t \right ) \\ y^{\prime }=-x-2 y+\sin \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.385 |
|
|
\[ {}x^{\prime }+3 x = {\mathrm e}^{-2 t} \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.407 |
|
|
\[ {}x^{\prime }-3 x = 3 t^{3}+3 t^{2}+2 t +1 \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.382 |
|
|
\[ {}x^{\prime }-x = \cos \left (t \right )-\sin \left (t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.471 |
|
|
\[ {}2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t} \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.428 |
|
|
\[ {}x^{\prime }+x = 2 \sin \left (t \right ) \] |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.45 |
|
|
\[ {}x^{\prime \prime } = 0 \] |
second_order_laplace |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.21 |
|
|
\[ {}x^{\prime \prime } = 1 \] |
second_order_laplace |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.259 |
|
|
\[ {}x^{\prime \prime } = \cos \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.361 |
|
|
\[ {}x^{\prime \prime }+x^{\prime } = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.23 |
|
|
\[ {}x^{\prime \prime }+x^{\prime } = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.222 |
|
|
\[ {}x^{\prime \prime }-x^{\prime } = 1 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.283 |
|
|
\[ {}x^{\prime \prime }+x = t \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.284 |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime } = 12 t +2 \] |
second_order_laplace |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.303 |
|
|
\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 2 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.335 |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 4 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.359 |
|
|
\[ {}2 x^{\prime \prime }-2 x^{\prime } = \left (t +1\right ) {\mathrm e}^{t} \] |
second_order_laplace |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.398 |
|
|
\[ {}x^{\prime \prime }+x = 2 \cos \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.482 |
|
|
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