|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {\ln \left (t y\right )}{1-t^{2}+y^{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.601 |
|
|
\[
{}y^{\prime } = \left (t^{2}+y^{2}\right )^{{3}/{2}}
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.597 |
|
|
\[
{}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}}
\] |
[_separable] |
✓ |
1.511 |
|
|
\[
{}y^{\prime } = \frac {\cot \left (t \right ) y}{y+1}
\] |
[_separable] |
✓ |
1.971 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
2.361 |
|
|
\[
{}y^{\prime } = -\frac {t}{2}+\frac {\sqrt {t^{2}+4 y}}{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.411 |
|
|
\[
{}y^{\prime } = -\frac {4 t}{y}
\] |
[_separable] |
✓ |
13.585 |
|
|
\[
{}y^{\prime } = 2 t y^{2}
\] |
[_separable] |
✓ |
2.137 |
|
|
\[
{}y^{\prime }+y^{3} = 0
\] |
[_quadrature] |
✓ |
22.193 |
|
|
\[
{}y^{\prime } = \frac {t^{2}}{y \left (t^{3}+1\right )}
\] |
[_separable] |
✓ |
2.706 |
|
|
\[
{}y^{\prime } = t y \left (3-y\right )
\] |
[_separable] |
✓ |
2.589 |
|
|
\[
{}y^{\prime } = y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.847 |
|
|
\[
{}y^{\prime } = -y \left (3-t y\right )
\] |
[_Bernoulli] |
✓ |
1.830 |
|
|
\[
{}y^{\prime }+2 y = \left \{\begin {array}{cc} 1 & 0\le t \le 1 \\ 0 & 1<t \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.911 |
|
|
\[
{}y^{\prime }+\left (\left \{\begin {array}{cc} 2 & 0\le t \le 1 \\ 1 & 1<t \end {array}\right .\right ) y = 0
\] |
[_separable] |
✓ |
2.138 |
|
|
\[
{}2 x +3+\left (2 y-2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.035 |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.851 |
|
|
\[
{}3 x^{2}-2 x y+2+\left (6 y^{2}-x^{2}+3\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.386 |
|
|
\[
{}2 x y^{2}+2 y+\left (2 x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.282 |
|
|
\[
{}y^{\prime } = -\frac {4 x +2 y}{2 x +3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.305 |
|
|
\[
{}y^{\prime } = -\frac {4 x -2 y}{2 x -3 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
11.682 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-2 y \sin \left (x \right )+\left ({\mathrm e}^{x} \cos \left (y\right )+2 \cos \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
7.502 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
9.553 |
|
|
\[
{}y \,{\mathrm e}^{x y} \cos \left (2 x \right )-2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+2 x +\left (x \,{\mathrm e}^{x y} \cos \left (2 x \right )-3\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
38.220 |
|
|
\[
{}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.576 |
|
|
\[
{}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.998 |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
4.046 |
|
|
\[
{}2 x -y+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.546 |
|
|
\[
{}9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.986 |
|
|
\[
{}x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.655 |
|
|
\[
{}\frac {\sin \left (y\right )}{y}-2 \,{\mathrm e}^{-x} \sin \left (x \right )+\frac {\left (\cos \left (y\right )+2 \,{\mathrm e}^{-x} \cos \left (x \right )\right ) y^{\prime }}{y} = 0
\] |
[NONE] |
✓ |
11.207 |
|
|
\[
{}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.390 |
|
|
\[
{}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.633 |
|
|
\[
{}3 x^{2} y+2 x y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
2.103 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x}+y-1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.374 |
|
|
\[
{}\frac {y^{\prime }}{\frac {x}{y}-\sin \left (y\right )} = 0
\] |
[_quadrature] |
✓ |
0.594 |
|
|
\[
{}y+\left (2 x y-{\mathrm e}^{-2 y}\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.811 |
|
|
\[
{}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.187 |
|
|
\[
{}\frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
1.307 |
|
|
\[
{}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.423 |
|
|
\[
{}3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
63.167 |
|
|
\[
{}y y^{\prime } = x +1
\] |
[_separable] |
✓ |
3.126 |
|
|
\[
{}\left (y^{4}+1\right ) y^{\prime } = x^{4}+1
\] |
[_separable] |
✓ |
1.451 |
|
|
\[
{}\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{3 x^{2} y+y^{3}} = 1
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
45.422 |
|
|
\[
{}x \left (-1+x \right ) y^{\prime } = y \left (y+1\right )
\] |
[_separable] |
✓ |
2.589 |
|
|
\[
{}\sqrt {x^{2}-y^{2}}+y = x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
92.378 |
|
|
\[
{}x y y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
79.296 |
|
|
\[
{}y^{\prime } = \frac {4 y-7 x}{5 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.507 |
|
|
\[
{}x y^{\prime }-4 \sqrt {y^{2}-x^{2}} = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
40.295 |
|
|
\[
{}y^{\prime } = \frac {y^{4}+2 x y^{3}-3 y^{2} x^{2}-2 x^{3} y}{2 y^{2} x^{2}-2 x^{3} y-2 x^{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.060 |
|
|
\[
{}\left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = y \,{\mathrm e}^{\frac {x}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.858 |
|
|
\[
{}x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
11.645 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1759.074 |
|
|
\[
{}t y^{\prime }+y = t^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.145 |
|
|
\[
{}y^{\prime } = y \left (t y^{3}-1\right )
\] |
[_Bernoulli] |
✓ |
1.345 |
|
|
\[
{}y^{\prime }+\frac {3 y}{t} = t^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.423 |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.765 |
|
|
\[
{}5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right )
\] |
[_separable] |
✓ |
39.443 |
|
|
\[
{}3 t y^{\prime }+9 y = 2 t y^{{5}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
23.960 |
|
|
\[
{}y^{\prime } = y+\sqrt {y}
\] |
[_quadrature] |
✓ |
2.916 |
|
|
\[
{}y^{\prime } = r y-k^{2} y^{2}
\] |
[_quadrature] |
✓ |
3.980 |
|
|
\[
{}y^{\prime } = a y+b y^{3}
\] |
[_quadrature] |
✓ |
8.723 |
|
|
\[
{}y^{\prime }+3 t y = 4-4 t^{2}+y^{2}
\] |
[_Riccati] |
✓ |
1.894 |
|
|
\[
{}\left (3 x-y \right ) x^{\prime }+9 y -2 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.247 |
|
|
\[
{}1 = \left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime }
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.395 |
|
|
\[
{}y^{\prime }-4 \,{\mathrm e}^{x} y^{2} = y
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.799 |
|
|
\[
{}x y^{\prime }+\left (x +1\right ) y = x
\] |
[_linear] |
✓ |
1.265 |
|
|
\[
{}y^{\prime } = \frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y}
\] |
[_Bernoulli] |
✓ |
36.187 |
|
|
\[
{}\frac {\sqrt {x}\, y^{\prime }}{y} = 1
\] |
[_separable] |
✓ |
1.581 |
|
|
\[
{}5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.238 |
|
|
\[
{}2 x y y^{\prime }+\ln \left (x \right ) = -y^{2}-1
\] |
[_exact, _Bernoulli] |
✓ |
1.934 |
|
|
\[
{}\left (2-x \right ) y^{\prime } = y+2 \left (2-x \right )^{5}
\] |
[_linear] |
✓ |
1.665 |
|
|
\[
{}x y^{\prime } = -\frac {1}{\ln \left (x \right )}
\] |
[_quadrature] |
✓ |
0.533 |
|
|
\[
{}x^{\prime } = \frac {2 x y +x^{2}}{3 y^{2}+2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
75.628 |
|
|
\[
{}4 x y y^{\prime } = 8 x^{2}+5 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
7.652 |
|
|
\[
{}y^{\prime }+y-y^{{1}/{4}} = 0
\] |
[_quadrature] |
✓ |
6.947 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x+4 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.553 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+\sin \left (t \right ) \\ y^{\prime }=-x+y-\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.366 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 t x+y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.031 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+4 \\ y^{\prime }=-2 x+y-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.793 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.798 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+t y \\ y^{\prime }=t x-y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.030 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+4 \\ y^{\prime }=-2 x+\sin \left (t \right ) y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.033 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.525 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.462 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.497 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+2 \sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.776 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y+2 t \\ y^{\prime }=x-3 y-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.555 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y+1 \\ y^{\prime }=x+y-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.855 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y-4 \\ y^{\prime }=x-y-6 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.813 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{4}-\frac {3 y}{4}+8 \\ y^{\prime }=\frac {x}{2}+y-\frac {23}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.639 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y-11 \\ y^{\prime }=-5 x+4 y-35 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.625 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-3 \\ y^{\prime }=-x+y+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.692 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+4 y-35 \\ y^{\prime }=-2 x+y-11 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.601 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.471 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.466 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=4 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.474 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.451 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.458 |
|