|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.102 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 y^{2} x^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.401 |
|
|
\[
{}y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.337 |
|
|
\[
{}x y-1+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
0.275 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.200 |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.526 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.260 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.579 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-2 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.586 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+4 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.590 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-x+2 y+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.448 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-7 y+10 \\ y^{\prime }=x-2 y-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.516 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (y\right ) \sec \left (x \right )}{x}
\] |
[_separable] |
✓ |
3.084 |
|
|
\[
{}y^{\prime } = x \left (\cos \left (y\right )+y\right )
\] |
[_separable] |
✓ |
1.924 |
|
|
\[
{}y^{\prime } = \frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x}
\] |
[_separable] |
✓ |
3.716 |
|
|
\[
{}y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right )
\] |
[_separable] |
✓ |
13.742 |
|
|
\[
{}y^{\prime } = y+1
\] |
[_quadrature] |
✓ |
1.374 |
|
|
\[
{}y^{\prime } = x +1
\] |
[_quadrature] |
✓ |
0.452 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.450 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.563 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.440 |
|
|
\[
{}y^{\prime } = 1+\frac {\sec \left (x \right )}{x}
\] |
[_quadrature] |
✓ |
0.761 |
|
|
\[
{}y^{\prime } = x +\frac {\sec \left (x \right ) y}{x}
\] |
[_linear] |
✓ |
6.469 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
2.639 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
2.267 |
|
|
\[
{}y^{\prime } = \frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )}
\] |
[_separable] |
✓ |
2.018 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✓ |
0.441 |
|
|
\[
{}y^{\prime } = \frac {-x y-1}{4 x^{3} y-2 x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.786 |
|
|
\[
{}\frac {{y^{\prime }}^{2}}{4}-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.411 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {y+1}{y^{2}}}
\] |
[_quadrature] |
✓ |
1687.005 |
|
|
\[
{}y^{\prime } = \sqrt {1-x^{2}-y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.580 |
|
|
\[
{}y^{\prime }+\frac {y}{3} = \frac {\left (1-2 x \right ) y^{4}}{3}
\] |
[_Bernoulli] |
✓ |
2.260 |
|
|
\[
{}y^{\prime } = \sqrt {y}+x
\] |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
10.400 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
40.740 |
|
|
\[
{}y = x y^{\prime }+x^{2} {y^{\prime }}^{2}
\] |
[_separable] |
✓ |
0.436 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.524 |
|
|
\[
{}x y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.443 |
|
|
\[
{}\frac {y^{\prime }}{x +y} = 0
\] |
[_quadrature] |
✓ |
0.496 |
|
|
\[
{}\frac {y^{\prime }}{x} = 0
\] |
[_quadrature] |
✓ |
0.449 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.439 |
|
|
\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.508 |
|
|
\[
{}y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.816 |
|
|
\[
{}2 t +3 x+\left (x+2\right ) x^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.546 |
|
|
\[
{}y^{\prime } = \frac {1}{1-y}
\] |
[_quadrature] |
✓ |
2.230 |
|
|
\[
{}p^{\prime } = a p-b p^{2}
\] |
[_quadrature] |
✓ |
5.109 |
|
|
\[
{}y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.407 |
|
|
\[
{}x f^{\prime }-f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}}
\] |
[_Clairaut] |
✓ |
5.423 |
|
|
\[
{}x y^{\prime }-2 y+b y^{2} = c \,x^{4}
\] |
[_rational, _Riccati] |
✓ |
2.250 |
|
|
\[
{}x y^{\prime }-y+y^{2} = x^{{2}/{3}}
\] |
[_rational, _Riccati] |
✓ |
11.816 |
|
|
\[
{}u^{\prime }+u^{2} = \frac {1}{x^{{4}/{5}}}
\] |
[_rational, _Riccati] |
✓ |
0.439 |
|
|
\[
{}y y^{\prime }-y = x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.945 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.947 |
|
|
\[
{}5 y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.777 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+4 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
14.192 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.832 |
|
|
\[
{}y = x {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.406 |
|
|
\[
{}y y^{\prime } = 1-x {y^{\prime }}^{3}
\] |
[_dAlembert] |
✓ |
0.300 |
|
|
\[
{}f^{\prime } = \frac {1}{f}
\] |
[_quadrature] |
✓ |
1.826 |
|
|
\[
{}t y^{\prime \prime }+4 y^{\prime } = t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.108 |
|
|
\[
{}\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.335 |
|
|
\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
3.406 |
|
|
\[
{}t y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.722 |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.834 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.867 |
|
|
\[
{}t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.141 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.894 |
|
|
\[
{}y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.096 |
|
|
\[
{}y^{\prime \prime } = f \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.482 |
|
|
\[
{}y^{\prime \prime } = k
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.152 |
|
|
\[
{}y^{\prime } = -4 \sin \left (x -y\right )-4
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
73.916 |
|
|
\[
{}y^{\prime }+\sin \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.297 |
|
|
\[
{}y^{\prime \prime } = 4 \sin \left (x \right )-4
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.196 |
|
|
\[
{}y y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.148 |
|
|
\[
{}y y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.724 |
|
|
\[
{}y y^{\prime \prime } = x
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.103 |
|
|
\[
{}y^{2} y^{\prime \prime } = x
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.107 |
|
|
\[
{}y^{2} y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.158 |
|
|
\[
{}3 y y^{\prime \prime } = \sin \left (x \right )
\] |
[NONE] |
✗ |
0.300 |
|
|
\[
{}3 y y^{\prime \prime }+y = 5
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
32.918 |
|
|
\[
{}a y y^{\prime \prime }+b y = c
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.676 |
|
|
\[
{}a y^{2} y^{\prime \prime }+b y^{2} = c
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.796 |
|
|
\[
{}a y y^{\prime \prime }+b y = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.622 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 x+4 y \\ y^{\prime }=-6 x-y \\ z^{\prime }=6 x+4 y+3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=3 x+7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.438 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.427 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+y \\ y^{\prime }=-4 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.441 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \\ z^{\prime }=z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.328 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-z \\ y^{\prime }=-x+2 z \\ z^{\prime }=-x-2 y+4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.375 |
|
|
\[
{}x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x
\] |
[_quadrature] |
✓ |
10.339 |
|
|
\[
{}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
0.836 |
|
|
\[
{}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
0.851 |
|
|
\[
{}y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}}
\] |
[_separable] |
✓ |
38.539 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.151 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
1.669 |
|
|
\[
{}z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.120 |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
41.197 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}-1
\] |
[_Riccati] |
✓ |
1.949 |
|
|
\[
{}y^{\prime } = 2 y \left (x \sqrt {y}-1\right )
\] |
[_Bernoulli] |
✓ |
1.569 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
67.281 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.162 |
|