|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.66 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.652 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = \delta \left (-1+t \right ) \] |
second_order_laplace |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.613 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right ) \] |
second_order_laplace |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.87 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.724 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \delta \left (-1+t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.547 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.013 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.358 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \] |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.475 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.496 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-5 y \\ y^{\prime }=4 x+8 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.996 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-7 y \\ y^{\prime }=5 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.978 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+4 y-9 z \\ y^{\prime }=6 x-y \\ z^{\prime }=10 x+4 y+3 z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
23.392 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+2 z \\ z^{\prime }=-x+z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
18.528 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y+z+t -1 \\ y^{\prime }=2 x+y-z-3 t^{2} \\ z^{\prime }=x+y+z+t^{2}-t +2 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
11.493 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+4 y+{\mathrm e}^{-t} \sin \left (2 t \right ) \\ y^{\prime }=5 x+9 z+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\ z^{\prime }=y+6 z-{\mathrm e}^{-t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
301.921 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x+2 y+{\mathrm e}^{t} \\ y^{\prime }=-x+3 y-{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.681 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\ y^{\prime }=4 x+y+z+2 \,{\mathrm e}^{5 t} \\ z^{\prime }=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
117.423 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y+2 z+{\mathrm e}^{-t}-3 t \\ y^{\prime }=3 x-4 y+z+2 \,{\mathrm e}^{-t}+t \\ z^{\prime }=-2 x+5 y+6 z+2 \,{\mathrm e}^{-t}-t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
208.704 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-7 y+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t} \\ y^{\prime }=x+y+8 \sin \left (t \right )+\left (1+2 t \right ) {\mathrm e}^{4 t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
9.974 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.529 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+5 y \\ y^{\prime }=-2 x+4 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.688 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+\frac {y}{4} \\ y^{\prime }=x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.477 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.49 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y+z \\ y^{\prime }=6 x-y \\ z^{\prime }=-x-2 y-z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.94 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=z+x \\ y^{\prime }=x+y \\ z^{\prime }=-2 x-z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.938 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=4 x+3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.464 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=x+3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.447 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+2 y \\ y^{\prime }=-\frac {5 x}{2}+2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.509 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-\frac {5 x}{2}+2 y \\ y^{\prime }=\frac {3 x}{4}-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.494 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=10 x-5 y \\ y^{\prime }=8 x-12 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.517 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-6 x+2 y \\ y^{\prime }=-3 x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.441 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=2 y \\ z^{\prime }=y-z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.622 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-7 y \\ y^{\prime }=5 x+10 y+4 z \\ z^{\prime }=5 y+2 z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.806 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+y \\ y^{\prime }=x+2 y+z \\ z^{\prime }=3 y-z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.794 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=z+x \\ y^{\prime }=y \\ z^{\prime }=z+x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.533 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x-y \\ y^{\prime }=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.841 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x-y \\ y^{\prime }=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.736 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+4 y+2 z \\ y^{\prime }=4 x-y-2 z \\ z^{\prime }=6 z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.751 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\frac {x}{2} \\ y^{\prime }=x-\frac {y}{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.385 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y+4 z \\ y^{\prime }=2 y \\ z^{\prime }=x+y+z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.66 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\ y^{\prime }=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\ z^{\prime }=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
95.264 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\ x_{2}^{\prime }=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\ x_{3}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{4}^{\prime }=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\ x_{5}^{\prime }=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
151.959 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=9 x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.371 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-6 x+5 y \\ y^{\prime }=-5 x+4 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.497 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+3 y \\ y^{\prime }=-3 x+5 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.52 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=12 x-9 y \\ y^{\prime }=4 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.522 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-y-z \\ y^{\prime }=x+y-z \\ z^{\prime }=x-y+z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.678 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x+2 y+4 z \\ y^{\prime }=2 x+2 z \\ z^{\prime }=4 x+2 y+3 z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.77 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+2 z \\ z^{\prime }=2 y+5 z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.576 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=3 y+z \\ z^{\prime }=-y+z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.624 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x+2 y-z \\ z^{\prime }=y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.434 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x+y \\ y^{\prime }=4 y+z \\ z^{\prime }=4 z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.366 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+4 y \\ y^{\prime }=-x+6 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.464 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=z \\ y^{\prime }=y \\ z^{\prime }=x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.489 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=6 x-y \\ y^{\prime }=5 x+2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.692 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.588 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x+y \\ y^{\prime }=-2 x+3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.664 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x+5 y \\ y^{\prime }=-2 x+6 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.743 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-5 y \\ y^{\prime }=5 x-4 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.663 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-8 y \\ y^{\prime }=x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.687 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=z \\ y^{\prime }=-z \\ z^{\prime }=y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.654 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y+2 z \\ y^{\prime }=3 x+6 z \\ z^{\prime }=-4 x-3 z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.451 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-12 y-14 z \\ y^{\prime }=x+2 y-3 z \\ z^{\prime }=x+y-2 z \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.919 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+3 y-7 \\ y^{\prime }=-x-2 y+5 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.918 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x+9 y+2 \\ y^{\prime }=-x+11 y+6 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.015 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.528 |
|
|
\[ {}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.503 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.602 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+x y^{\prime }-y^{2}-y = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.618 |
|
|
\[ {}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.421 |
|
|
\[ {}{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.398 |
|
|
\[ {}x {y^{\prime }}^{2}-\left (1+x y\right ) y^{\prime }+y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.282 |
|
|
\[ {}{y^{\prime }}^{2}-x^{2} y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.465 |
|
|
\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2} \] |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.195 |
|
|
\[ {}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.532 |
|
|
\[ {}{y^{\prime }}^{2}-x y \left (x +y\right ) y^{\prime }+x^{3} y^{3} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.546 |
|
|
\[ {}\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0 \] |
quadrature, homogeneousTypeD2 |
[_quadrature] |
✓ |
✓ |
0.836 |
|
|
\[ {}\left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2} \] |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.11 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.536 |
|
|
\[ {}\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 x^{2} y^{2} \] |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.7 |
|
|
\[ {}\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+y \left (y-x \right ) = 0 \] |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.439 |
|
|
\[ {}x y \left (x^{2}+y^{2}\right ) \left ({y^{\prime }}^{2}-1\right ) = y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right ) \] |
homogeneousTypeD2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.103 |
|
|
\[ {}x {y^{\prime }}^{3}-\left (x^{2}+x +y\right ) {y^{\prime }}^{2}+\left (x^{2}+x y+y\right ) y^{\prime }-x y = 0 \] |
quadrature, separable |
[_quadrature] |
✓ |
✓ |
0.477 |
|
|
\[ {}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.403 |
|
|
\[ {}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0 \] |
dAlembert |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.368 |
|
|
\[ {}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
4.311 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.498 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }+y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.262 |
|
|
\[ {}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 y x^{4} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.935 |
|
|
\[ {}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
6.27 |
|
|
\[ {}4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
22.549 |
|
|
\[ {}{y^{\prime }}^{3}+x {y^{\prime }}^{2}-y = 0 \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
151.773 |
|
|
\[ {}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
114.33 |
|
|
\[ {}{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
5.641 |
|
|
\[ {}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 y x^{4} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
4.579 |
|
|
\[ {}2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
108.481 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }+y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.292 |
|
|
\[ {}y = x y^{\prime }+k {y^{\prime }}^{2} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.302 |
|
|
\[ {}x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
4.955 |
|
|
|
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|
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