|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {2 y}{x}
\] |
[_separable] |
✓ |
1.605 |
|
|
\[
{}y^{\prime } = \frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )}
\] |
[_separable] |
✓ |
1.681 |
|
|
\[
{}y^{\prime } = \frac {1}{x}
\] |
[_quadrature] |
✓ |
0.280 |
|
|
\[
{}y^{\prime } = \frac {-x y-1}{4 x^{3} y-2 x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.600 |
|
|
\[
{}\frac {{y^{\prime }}^{2}}{4}-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.356 |
|
|
\[
{}y^{\prime } = \sqrt {\frac {1+y}{y^{2}}}
\] |
[_quadrature] |
✓ |
1454.228 |
|
|
\[
{}y^{\prime } = \sqrt {1-x^{2}-y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.552 |
|
|
\[
{}y^{\prime }+\frac {y}{3} = \frac {\left (-2 x +1\right ) y^{4}}{3}
\] |
[_Bernoulli] |
✓ |
2.000 |
|
|
\[
{}y^{\prime } = \sqrt {y}+x
\] |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
4.833 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.785 |
|
|
\[
{}y = x y^{\prime }+x^{2} {y^{\prime }}^{2}
\] |
[_separable] |
✓ |
0.930 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.385 |
|
|
\[
{}x y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.382 |
|
|
\[
{}\frac {y^{\prime }}{x +y} = 0
\] |
[_quadrature] |
✓ |
0.375 |
|
|
\[
{}\frac {y^{\prime }}{x} = 0
\] |
[_quadrature] |
✓ |
0.381 |
|
|
\[
{}y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.372 |
|
|
\[
{}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
0.487 |
|
|
\[
{}y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.282 |
|
|
\[
{}2 t +3 x+\left (x+2\right ) x^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.351 |
|
|
\[
{}y^{\prime } = \frac {1}{1-y}
\] |
[_quadrature] |
✓ |
1.563 |
|
|
\[
{}p^{\prime } = a p-b p^{2}
\] |
[_quadrature] |
✓ |
1.928 |
|
|
\[
{}y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
1.653 |
|
|
\[
{}f^{\prime } x -f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}}
\] |
[_Clairaut] |
✓ |
3.533 |
|
|
\[
{}x y^{\prime }-2 y+b y^{2} = c \,x^{4}
\] |
[_rational, _Riccati] |
✓ |
1.505 |
|
|
\[
{}x y^{\prime }-y+y^{2} = x^{{2}/{3}}
\] |
[_rational, _Riccati] |
✓ |
11.432 |
|
|
\[
{}u^{\prime }+u^{2} = \frac {1}{x^{{4}/{5}}}
\] |
[_rational, _Riccati] |
✓ |
0.335 |
|
|
\[
{}y y^{\prime }-y = x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.852 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.839 |
|
|
\[
{}5 y^{\prime \prime }+2 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.703 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+4 y = 1
\] |
[[_2nd_order, _missing_x]] |
✓ |
13.559 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
73.062 |
|
|
\[
{}y = x {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.390 |
|
|
\[
{}y y^{\prime } = 1-x {y^{\prime }}^{3}
\] |
[_dAlembert] |
✓ |
0.233 |
|
|
\[
{}f^{\prime } = \frac {1}{f}
\] |
[_quadrature] |
✓ |
1.254 |
|
|
\[
{}t y^{\prime \prime }+4 y^{\prime } = t^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.158 |
|
|
\[
{}\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.333 |
|
|
\[
{}t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.006 |
|
|
\[
{}t y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.867 |
|
|
\[
{}t^{2} y^{\prime \prime }-2 y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.956 |
|
|
\[
{}y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.959 |
|
|
\[
{}t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.356 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.305 |
|
|
\[
{}y^{\prime \prime } = 1
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.712 |
|
|
\[
{}y^{\prime \prime } = f \left (t \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.654 |
|
|
\[
{}y^{\prime \prime } = k
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.780 |
|
|
\[
{}y^{\prime } = -4 \sin \left (x -y\right )-4
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
73.531 |
|
|
\[
{}y^{\prime }+\sin \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.389 |
|
|
\[
{}y^{\prime \prime } = 4 \sin \left (x \right )-4
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.639 |
|
|
\[
{}y y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.142 |
|
|
\[
{}y y^{\prime \prime } = 1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.530 |
|
|
\[
{}y y^{\prime \prime } = x
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.080 |
|
|
\[
{}y^{2} y^{\prime \prime } = x
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.124 |
|
|
\[
{}y^{2} y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.147 |
|
|
\[
{}3 y y^{\prime \prime } = \sin \left (x \right )
\] |
[NONE] |
✗ |
0.145 |
|
|
\[
{}3 y y^{\prime \prime }+y = 5
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
483.769 |
|
|
\[
{}a y y^{\prime \prime }+b y = c
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.091 |
|
|
\[
{}a y^{2} y^{\prime \prime }+b y^{2} = c
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.484 |
|
|
\[
{}a y y^{\prime \prime }+b y = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.615 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 x+4 y \\ y^{\prime }=-6 x-y \\ z^{\prime }=6 x+4 y+3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.364 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=3 x+7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.304 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=2 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.303 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+y \\ y^{\prime }=-4 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.314 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \\ z^{\prime }=z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.280 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y-z \\ y^{\prime }=-x+2 z \\ z^{\prime }=-x-2 y+4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.355 |
|
|
\[
{}x^{\prime } = 4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x
\] |
[_quadrature] |
✓ |
5.292 |
|
|
\[
{}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.343 |
|
|
\[
{}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.300 |
|
|
\[
{}y^{\prime } = \frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}}
\] |
[_separable] |
✓ |
114.593 |
|
|
\[
{}y^{\prime } = y^{2}+x^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.019 |
|
|
\[
{}y^{\prime } = 2 \sqrt {y}
\] |
[_quadrature] |
✓ |
1.283 |
|
|
\[
{}z^{\prime \prime }+3 z^{\prime }+2 z = 24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.067 |
|
|
\[
{}y^{\prime } = \sqrt {1-y^{2}}
\] |
[_quadrature] |
✓ |
39.146 |
|
|
\[
{}y^{\prime } = -1+x^{2}+y^{2}
\] |
[_Riccati] |
✓ |
1.810 |
|
|
\[
{}y^{\prime } = 2 y \left (x \sqrt {y}-1\right )
\] |
[_Bernoulli] |
✓ |
1.373 |
|
|
\[
{}y^{\prime \prime } = \frac {1}{y}-\frac {x y^{\prime }}{y^{2}}
\] |
[[_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]] |
✓ |
68.440 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.141 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.141 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.018 |
|
|
\[
{}y^{\prime \prime }-y y^{\prime } = 2 x
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
5.912 |
|
|
\[
{}y^{\prime }-y^{2}-x -x^{2} = 0
\] |
[_Riccati] |
✓ |
4.816 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.984 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-2 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.986 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-3 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.996 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{2}-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.559 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{3}+2 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.697 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{4}-6 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.726 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{5}+24 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.688 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.983 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.470 |
|
|
\[
{}y^{\prime \prime }-x y^{\prime }-x y-x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.570 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.656 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.627 |
|
|
\[
{}y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.606 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.257 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{2} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.258 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.356 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{2}-1 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.359 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-x y-x^{2}-2 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.360 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }-x y-x^{2}-4 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.353 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-x y-x^{3}+1 = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.306 |
|