|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.303 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 y^{2} x^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.190 |
|
|
\[
{}y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.350 |
|
|
\[
{}x y-1+x^{2} y^{\prime } = 0
\] |
[_linear] |
✓ |
0.293 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.467 |
|
|
\[
{}y^{\prime \prime }+16 y = 4 \cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.760 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.557 |
|
|
\[
{}y^{\prime \prime }+y = \tan \left (x \right )^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.776 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-2 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.555 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+4 y \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.569 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-x+2 y+4 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.481 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-7 y+10 \\ y^{\prime }=x-2 y-2 \,{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.529 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (y\right ) \sec \left (x \right )}{x}
\] |
[_separable] |
✓ |
2.586 |
|
|
\[
{}y^{\prime } = x \left (\cos \left (y\right )+y\right )
\] |
[_separable] |
✓ |
1.738 |
|
|
\[
{}y^{\prime } = \frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x}
\] |
[_separable] |
✓ |
3.333 |
|
|
\[
{}y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right )
\] |
[_separable] |
✓ |
12.026 |
|
|
\[
{}y^{\prime } = 1+y
\] |
[_quadrature] |
✓ |
1.181 |
|
|
\[
{}y^{\prime } = x +1
\] |
[_quadrature] |
✓ |
0.465 |
|
|
\[
{}y^{\prime } = x
\] |
[_quadrature] |
✓ |
0.454 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
1.352 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.720 |
|
|
\[
{}y^{\prime } = 1+\frac {\sec \left (x \right )}{x}
\] |
[_quadrature] |
✓ |
1.019 |
|
|
\[
{}y^{\prime } = x +\frac {\sec \left (x \right ) y}{x}
\] |
[_linear] |
✓ |
7.385 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
2.802 |
|
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
2.185 |
|
|
\[
{}y^{\prime } = \frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )}
\] |
[_separable] |
✓ |
1.796 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✓ |
0.466 |
|
|
\[
{}y^{\prime } = \frac {-x y-1}{4 x^{3} y-2 x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.684 |
|
|
\[
{}\frac {{y^{\prime }}^{2}}{4}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.349 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {1+y}{y^{2}}}
\] |
[_quadrature] |
✓ |
1445.155 |
|
|
\[
{}y^{\prime } = \sqrt {1-x^{2}-y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.782 |
|
|
\[
{}y^{\prime }+\frac {y}{3} = \frac {\left (1-2 x \right ) y^{4}}{3}
\] |
[_Bernoulli] |
✓ |
2.319 |
|
|
\[
{}y^{\prime } = \sqrt {y}+x
\] |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
5.065 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
37.975 |
|
|
\[
{}y = y^{\prime } x +x^{2} {y^{\prime }}^{2}
\] |
[_separable] |
✓ |
0.967 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.699 |
|
|
\[
{}y^{\prime } x = 0
\] |
[_quadrature] |
✓ |
0.677 |
|
|
\[
{}\frac {y^{\prime }}{x +y} = 0
\] |
[_quadrature] |
✓ |
0.702 |
|
|
\[
{}\frac {y^{\prime }}{x} = 0
\] |
[_quadrature] |
✓ |
0.675 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.659 |
|
|
\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.506 |
|
|
\[
{}y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.829 |
|
|
\[
{}2 t +3 x+\left (x+2\right ) x^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.633 |
|
|
\[
{}y^{\prime } = \frac {1}{1-y}
\] |
[_quadrature] |
✓ |
1.807 |
|
|
\[
{}p^{\prime } = a p-b p^{2}
\] |
[_quadrature] |
✓ |
1.737 |
|
|
\[
{}y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
1.984 |
|
|
\[
{}x f^{\prime }-f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}}
\] |
[_Clairaut] |
✓ |
3.653 |
|
|
\[
{}y^{\prime } x -2 y+b y^{2} = c \,x^{4}
\] |
[_rational, _Riccati] |
✓ |
2.563 |
|
|
\[
{}y^{\prime } x -y+y^{2} = x^{{2}/{3}}
\] |
[_rational, _Riccati] |
✓ |
11.846 |
|
|
\[
{}u^{\prime }+u^{2} = \frac {1}{x^{{4}/{5}}}
\] |
[_rational, _Riccati] |
✓ |
0.391 |
|
|
\[
{}y y^{\prime }-y = x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.329 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.252 |
|
|
\[
{}5 y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.280 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+4 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
15.158 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
75.902 |
|
|
\[
{}y = x {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.489 |
|
|
\[
{}y y^{\prime } = 1-x {y^{\prime }}^{3}
\] |
[_dAlembert] |
✓ |
0.256 |
|
|
\[
{}f^{\prime } = \frac {1}{f}
\] |
[_quadrature] |
✓ |
1.643 |
|
|
\[
{}t y^{\prime \prime }+4 y^{\prime } = t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.364 |
|
|
\[
{}\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.431 |
|
|
\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.086 |
|
|
\[
{}t y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.903 |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.036 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.881 |
|
|
\[
{}t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.387 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.080 |
|
|
\[
{}y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.484 |
|
|
\[
{}y^{\prime \prime } = f \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.682 |
|
|
\[
{}y^{\prime \prime } = k
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.641 |
|
|
\[
{}y^{\prime } = -4 \sin \left (x -y\right )-4
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
75.256 |
|
|
\[
{}y^{\prime }+\sin \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.692 |
|
|
\[
{}y^{\prime \prime } = 4 \sin \left (x \right )-4
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.388 |
|
|
\[
{}y y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.101 |
|
|
\[
{}y y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.521 |
|
|
\[
{}y y^{\prime \prime } = x
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.122 |
|
|
\[
{}y^{2} y^{\prime \prime } = x
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.126 |
|
|
\[
{}y^{2} y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.201 |
|
|
\[
{}3 y y^{\prime \prime } = \sin \left (x \right )
\] |
[NONE] |
✗ |
0.240 |
|
|
\[
{}3 y y^{\prime \prime }+y = 5
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
494.702 |
|
|
\[
{}a y y^{\prime \prime }+b y = c
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.086 |
|
|
\[
{}a y^{2} y^{\prime \prime }+b y^{2} = c
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.560 |
|
|
\[
{}a y y^{\prime \prime }+b y = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
2.906 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 x+4 y \\ y^{\prime }=-6 x-y \\ z^{\prime }=6 x+4 y+3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.396 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=3 x+7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.406 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.382 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+y \\ y^{\prime }=-4 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \\ z^{\prime }=z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.322 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-z \\ y^{\prime }=-x+2 z \\ z^{\prime }=-x-2 y+4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.353 |
|
|
\[
{}x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x
\] |
[_quadrature] |
✓ |
5.440 |
|
|
\[
{}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.316 |
|
|
\[
{}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.162 |
|
|
\[
{}y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}}
\] |
[_separable] |
✓ |
118.786 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.112 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
1.214 |
|
|
\[
{}z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.371 |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
39.910 |
|
|
\[
{}y^{\prime } = x^{2}+y^{2}-1
\] |
[_Riccati] |
✓ |
1.800 |
|
|
\[
{}y^{\prime } = 2 y \left (x \sqrt {y}-1\right )
\] |
[_Bernoulli] |
✓ |
1.512 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}
\] |
[[_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]] |
✓ |
68.701 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.592 |
|