|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x \left (a x +1\right ) y^{\prime }+a -y = 0
\] |
[_separable] |
✓ |
1.277 |
|
|
\[
{}\left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3} = 0
\] |
[_rational, _Abel] |
✗ |
1.331 |
|
|
\[
{}x^{3} y^{\prime } = a +b \,x^{2} y
\] |
[_linear] |
✓ |
1.391 |
|
|
\[
{}x^{3} y^{\prime } = 3-x^{2}+x^{2} y
\] |
[_linear] |
✓ |
0.980 |
|
|
\[
{}x^{3} y^{\prime } = x^{4}+y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.381 |
|
|
\[
{}x^{3} y^{\prime } = y \left (y+x^{2}\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.010 |
|
|
\[
{}x^{3} y^{\prime } = x^{2} \left (-1+y\right )+y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.123 |
|
|
\[
{}x^{3} y^{\prime } = \left (x +1\right ) y^{2}
\] |
[_separable] |
✓ |
1.667 |
|
|
\[
{}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.826 |
|
|
\[
{}x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.896 |
|
|
\[
{}x^{3} y^{\prime } = \left (2 x^{2}+y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
95.718 |
|
|
\[
{}x^{3} y^{\prime } = \cos \left (y\right ) \left (\cos \left (y\right )-2 x^{2} \sin \left (y\right )\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.672 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{2}+y
\] |
[_linear] |
✓ |
1.335 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{2}+y
\] |
[_linear] |
✓ |
1.727 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{3}+y
\] |
[_linear] |
✓ |
1.261 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = a -x^{2} y
\] |
[_linear] |
✓ |
1.665 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = \left (-x^{2}+1\right ) y
\] |
[_separable] |
✓ |
1.247 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = \left (x^{2}-x +1\right ) y
\] |
[_separable] |
✓ |
1.733 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{3}+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
1.335 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime } = x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
3.201 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = 2-4 x^{2} y
\] |
[_linear] |
✓ |
1.615 |
|
|
\[
{}x \left (x^{2}+1\right ) y^{\prime } = x -\left (5 x^{2}+3\right ) y
\] |
[_linear] |
✓ |
1.371 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime }+x^{2}+\left (-x^{2}+1\right ) y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
144.013 |
|
|
\[
{}x^{2} \left (1-x \right ) y^{\prime } = \left (2-x \right ) x y-y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.749 |
|
|
\[
{}2 x^{3} y^{\prime } = \left (x^{2}-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
96.299 |
|
|
\[
{}2 x^{3} y^{\prime } = \left (3 x^{2}+a y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
20.509 |
|
|
\[
{}6 x^{3} y^{\prime } = 4 x^{2} y+\left (1-3 x \right ) y^{4}
\] |
[_rational, _Bernoulli] |
✓ |
3.119 |
|
|
\[
{}x \left (c \,x^{2}+b x +a \right ) y^{\prime }+x^{2}-\left (c \,x^{2}+b x +a \right ) y = y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
3.157 |
|
|
\[
{}x^{4} y^{\prime } = \left (x^{3}+y\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.181 |
|
|
\[
{}x^{4} y^{\prime }+a^{2}+x^{4} y^{2} = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
1.763 |
|
|
\[
{}x^{4} y^{\prime }+x^{3} y+\csc \left (y x \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
48.883 |
|
|
\[
{}\left (-x^{4}+1\right ) y^{\prime } = 2 x \left (1-y^{2}\right )
\] |
[_separable] |
✓ |
1.754 |
|
|
\[
{}x \left (-x^{3}+1\right ) y^{\prime } = 2 x -\left (-4 x^{3}+1\right ) y
\] |
[_linear] |
✓ |
1.688 |
|
|
\[
{}x \left (-x^{3}+1\right ) y^{\prime } = x^{2}+\left (1-2 y x \right ) y
\] |
[_rational, _Riccati] |
✓ |
1.528 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime } = \left (x -3 x^{3} y\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
1.465 |
|
|
\[
{}x \left (-2 x^{3}+1\right ) y^{\prime } = 2 \left (-x^{3}+1\right ) y
\] |
[_separable] |
✓ |
1.665 |
|
|
\[
{}\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
[_rational, _Riccati] |
✓ |
4.543 |
|
|
\[
{}x^{5} y^{\prime } = 1-3 x^{4} y
\] |
[_linear] |
✓ |
1.463 |
|
|
\[
{}x \left (-x^{4}+1\right ) y^{\prime } = 2 x \left (x^{2}-y^{2}\right )+\left (-x^{4}+1\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
1.633 |
|
|
\[
{}x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3} = 0
\] |
[_rational, _Abel] |
✗ |
0.648 |
|
|
\[
{}x^{n} y^{\prime } = a +b \,x^{n -1} y
\] |
[_linear] |
✓ |
1.200 |
|
|
\[
{}x^{n} y^{\prime } = x^{2 n -1}-y^{2}
\] |
[_Riccati] |
✓ |
1.847 |
|
|
\[
{}x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (-n +1\right ) x^{n -1} = 0
\] |
[_Riccati] |
✗ |
50.027 |
|
|
\[
{}x^{n} y^{\prime } = a^{2} x^{2 n -2}+b^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
4.406 |
|
|
\[
{}x^{n} y^{\prime } = x^{n -1} \left (a \,x^{2 n}+n y-b y^{2}\right )
\] |
[_rational, _Riccati] |
✓ |
2.942 |
|
|
\[
{}x^{k} y^{\prime } = a \,x^{m}+b y^{n}
\] |
[_Chini] |
✗ |
0.792 |
|
|
\[
{}\sqrt {x^{2}+1}\, y^{\prime } = 2 x -y
\] |
[_linear] |
✓ |
2.033 |
|
|
\[
{}y^{\prime } \sqrt {-x^{2}+1} = 1+y^{2}
\] |
[_separable] |
✓ |
3.046 |
|
|
\[
{}\left (x -\sqrt {x^{2}+1}\right ) y^{\prime } = y+\sqrt {1+y^{2}}
\] |
[_separable] |
✓ |
3.174 |
|
|
\[
{}y^{\prime } \sqrt {a^{2}+x^{2}}+x +y = \sqrt {a^{2}+x^{2}}
\] |
[_linear] |
✓ |
2.072 |
|
|
\[
{}y^{\prime } \sqrt {b^{2}+x^{2}} = \sqrt {y^{2}+a^{2}}
\] |
[_separable] |
✓ |
15.937 |
|
|
\[
{}y^{\prime } \sqrt {b^{2}-x^{2}} = \sqrt {a^{2}-y^{2}}
\] |
[_separable] |
✓ |
18.165 |
|
|
\[
{}x y^{\prime } \sqrt {a^{2}+x^{2}} = y \sqrt {b^{2}+y^{2}}
\] |
[_separable] |
✓ |
2.664 |
|
|
\[
{}x y^{\prime } \sqrt {-a^{2}+x^{2}} = y \sqrt {y^{2}-b^{2}}
\] |
[_separable] |
✓ |
26.319 |
|
|
\[
{}y^{\prime } \sqrt {X}+\sqrt {Y} = 0
\] |
[_quadrature] |
✓ |
1.086 |
|
|
\[
{}y^{\prime } \sqrt {X} = \sqrt {Y}
\] |
[_quadrature] |
✓ |
0.346 |
|
|
\[
{}x^{{3}/{2}} y^{\prime } = a +b \,x^{{3}/{2}} y^{2}
\] |
[_rational, [_Riccati, _special]] |
✓ |
3.257 |
|
|
\[
{}y^{\prime } \sqrt {x^{3}+1} = \sqrt {1+y^{3}}
\] |
[_separable] |
✓ |
6.174 |
|
|
\[
{}y^{\prime } \sqrt {x \left (1-x \right ) \left (-a x +1\right )} = \sqrt {y \left (1-y\right ) \left (1-a y\right )}
\] |
[_separable] |
✓ |
13.097 |
|
|
\[
{}y^{\prime } \sqrt {-x^{4}+1} = \sqrt {1-y^{4}}
\] |
[_separable] |
✓ |
8.191 |
|
|
\[
{}y^{\prime } \sqrt {x^{4}+x^{2}+1} = \sqrt {1+y^{2}+y^{4}}
\] |
[_separable] |
✓ |
7.674 |
|
|
\[
{}y^{\prime } \sqrt {X} = 0
\] |
[_quadrature] |
✓ |
1.069 |
|
|
\[
{}y^{\prime } \sqrt {X}+\sqrt {Y} = 0
\] |
[_quadrature] |
✓ |
0.401 |
|
|
\[
{}y^{\prime } \sqrt {X} = \sqrt {Y}
\] |
[_quadrature] |
✓ |
0.342 |
|
|
\[
{}y^{\prime } \left (x^{3}+1\right )^{{2}/{3}}+\left (1+y^{3}\right )^{{2}/{3}} = 0
\] |
[_separable] |
✓ |
3.830 |
|
|
\[
{}y^{\prime } \left (4 x^{3}+\operatorname {a1} x +\operatorname {a0} \right )^{{2}/{3}}+\left (\operatorname {a0} +\operatorname {a1} y+4 y^{3}\right )^{{2}/{3}} = 0
\] |
[_separable] |
✓ |
4.200 |
|
|
\[
{}X^{{2}/{3}} y^{\prime } = Y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
0.477 |
|
|
\[
{}y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right ) = y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right )
\] |
[_Bernoulli] |
✓ |
56.442 |
|
|
\[
{}\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime } = \tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y
\] |
[_separable] |
✓ |
12.704 |
|
|
\[
{}\left (1-\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
4.066 |
|
|
\[
{}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = 0
\] |
[_separable] |
✓ |
4.190 |
|
|
\[
{}\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )+\operatorname {a1} y \sin \left (2 x \right ) = 0
\] |
[_linear] |
✓ |
24.516 |
|
|
\[
{}\left (x -{\mathrm e}^{x}\right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (1-{\mathrm e}^{x}\right ) y = 0
\] |
[_linear] |
✓ |
3.059 |
|
|
\[
{}y^{\prime } x \ln \left (x \right ) = a x \left (1+\ln \left (x \right )\right )-y
\] |
[_linear] |
✓ |
2.875 |
|
|
\[
{}y y^{\prime }+x = 0
\] |
[_separable] |
✓ |
4.263 |
|
|
\[
{}y y^{\prime }+x \,{\mathrm e}^{x^{2}} = 0
\] |
[_separable] |
✓ |
1.763 |
|
|
\[
{}y y^{\prime }+x^{3}+y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.561 |
|
|
\[
{}y y^{\prime }+a x +b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
17.993 |
|
|
\[
{}y y^{\prime }+x \,{\mathrm e}^{-x} \left (1+y\right ) = 0
\] |
[_separable] |
✓ |
3.292 |
|
|
\[
{}y y^{\prime }+f \left (x \right ) = g \left (x \right ) y
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.520 |
|
|
\[
{}y y^{\prime }+4 \left (x +1\right ) x +y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.042 |
|
|
\[
{}y y^{\prime } = a x +b y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
2.011 |
|
|
\[
{}y y^{\prime } = b \cos \left (x +c \right )+a y^{2}
\] |
[_Bernoulli] |
✓ |
4.961 |
|
|
\[
{}y y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}
\] |
[_quadrature] |
✓ |
5.375 |
|
|
\[
{}y y^{\prime } = a x +b x y^{2}
\] |
[_separable] |
✓ |
3.700 |
|
|
\[
{}y y^{\prime } = \csc \left (x \right )^{2}-y^{2} \cot \left (x \right )
\] |
[_Bernoulli] |
✓ |
24.846 |
|
|
\[
{}y y^{\prime } = \sqrt {y^{2}+a^{2}}
\] |
[_quadrature] |
✓ |
1.740 |
|
|
\[
{}y y^{\prime } = \sqrt {y^{2}-a^{2}}
\] |
[_quadrature] |
✓ |
2.128 |
|
|
\[
{}y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right ) = 0
\] |
[NONE] |
✗ |
1.406 |
|
|
\[
{}\left (1+y\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
12.258 |
|
|
\[
{}\left (1+y\right ) y^{\prime } = x^{2} \left (1-y\right )
\] |
[_separable] |
✓ |
1.736 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.582 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.661 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.414 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.014 |
|
|
\[
{}1-y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.828 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = y \left (2 y x +1\right )
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.977 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+\tan \left (y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.875 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = \left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.671 |
|
|
\[
{}\left (x +y+1\right ) y^{\prime }+1+4 x +3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.547 |
|