|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } \sqrt {x^{4}+x^{2}+1} = \sqrt {1+y^{2}+y^{4}}
\] |
[_separable] |
✓ |
3.791 |
|
|
\[
{}y^{\prime } \sqrt {X} = 0
\] |
[_quadrature] |
✓ |
0.534 |
|
|
\[
{}y^{\prime } \sqrt {X}+\sqrt {Y} = 0
\] |
[_quadrature] |
✓ |
0.424 |
|
|
\[
{}y^{\prime } \sqrt {X} = \sqrt {Y}
\] |
[_quadrature] |
✓ |
0.426 |
|
|
\[
{}y^{\prime } \left (x^{3}+1\right )^{{2}/{3}}+\left (1+y^{3}\right )^{{2}/{3}} = 0
\] |
[_separable] |
✓ |
3.631 |
|
|
\[
{}y^{\prime } \left (4 x^{3}+\operatorname {a1} x +\operatorname {a0} \right )^{{2}/{3}}+\left (\operatorname {a0} +\operatorname {a1} y+4 y^{3}\right )^{{2}/{3}} = 0
\] |
[_separable] |
✓ |
2.335 |
|
|
\[
{}X^{{2}/{3}} y^{\prime } = Y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
0.543 |
|
|
\[
{}y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right ) = y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right )
\] |
[_Bernoulli] |
✓ |
21.041 |
|
|
\[
{}\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime } = \tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y
\] |
[_separable] |
✓ |
8.496 |
|
|
\[
{}\left (1-\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
3.320 |
|
|
\[
{}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = 0
\] |
[_separable] |
✓ |
3.668 |
|
|
\[
{}\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )+\operatorname {a1} y \sin \left (2 x \right ) = 0
\] |
[_linear] |
✓ |
12.961 |
|
|
\[
{}\left (x -{\mathrm e}^{x}\right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (1-{\mathrm e}^{x}\right ) y = 0
\] |
[_linear] |
✓ |
1.791 |
|
|
\[
{}y^{\prime } x \ln \left (x \right ) = a x \left (1+\ln \left (x \right )\right )-y
\] |
[_linear] |
✓ |
1.549 |
|
|
\[
{}y y^{\prime }+x = 0
\] |
[_separable] |
✓ |
4.033 |
|
|
\[
{}y y^{\prime }+x \,{\mathrm e}^{x^{2}} = 0
\] |
[_separable] |
✓ |
2.003 |
|
|
\[
{}y y^{\prime }+x^{3}+y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.737 |
|
|
\[
{}y y^{\prime }+a x +b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.145 |
|
|
\[
{}y y^{\prime }+x \,{\mathrm e}^{-x} \left (y+1\right ) = 0
\] |
[_separable] |
✓ |
2.167 |
|
|
\[
{}y y^{\prime }+f \left (x \right ) = g \left (x \right ) y
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.128 |
|
|
\[
{}y y^{\prime }+4 x \left (x +1\right )+y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.344 |
|
|
\[
{}y y^{\prime } = a x +b y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
1.581 |
|
|
\[
{}y y^{\prime } = b \cos \left (x +c \right )+a y^{2}
\] |
[_Bernoulli] |
✓ |
3.426 |
|
|
\[
{}y y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}
\] |
[_quadrature] |
✓ |
2.440 |
|
|
\[
{}y y^{\prime } = a x +b x y^{2}
\] |
[_separable] |
✓ |
2.127 |
|
|
\[
{}y y^{\prime } = \csc \left (x \right )^{2}-y^{2} \cot \left (x \right )
\] |
[_Bernoulli] |
✓ |
15.643 |
|
|
\[
{}y y^{\prime } = \sqrt {y^{2}+a^{2}}
\] |
[_quadrature] |
✓ |
2.411 |
|
|
\[
{}y y^{\prime } = \sqrt {y^{2}-a^{2}}
\] |
[_quadrature] |
✓ |
2.190 |
|
|
\[
{}y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right ) = 0
\] |
[NONE] |
✗ |
2.856 |
|
|
\[
{}\left (y+1\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.419 |
|
|
\[
{}\left (y+1\right ) y^{\prime } = x^{2} \left (1-y\right )
\] |
[_separable] |
✓ |
1.509 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.941 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.091 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
38.869 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.299 |
|
|
\[
{}1-y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.372 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = \left (2 x y+1\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.678 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+\tan \left (y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.574 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = \left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.082 |
|
|
\[
{}\left (1+x +y\right ) y^{\prime }+1+4 x +3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.736 |
|
|
\[
{}\left (x +y+2\right ) y^{\prime } = 1-x -y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.888 |
|
|
\[
{}\left (3-x -y\right ) y^{\prime } = 1+x -3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.781 |
|
|
\[
{}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.856 |
|
|
\[
{}\left (y+2 x \right ) y^{\prime }+x -2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
40.447 |
|
|
\[
{}\left (2 x -y+2\right ) y^{\prime }+3+6 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.925 |
|
|
\[
{}\left (3+2 x -y\right ) y^{\prime }+2 = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.617 |
|
|
\[
{}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.675 |
|
|
\[
{}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.289 |
|
|
\[
{}\left (1-3 x +y\right ) y^{\prime } = 2 x -2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
94.539 |
|
|
\[
{}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.531 |
|
|
\[
{}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.776 |
|
|
\[
{}\left (6-4 x -y\right ) y^{\prime } = 2 x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.163 |
|
|
\[
{}\left (1+5 x -y\right ) y^{\prime }+5+x -5 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.621 |
|
|
\[
{}\left (a +b x +y\right ) y^{\prime }+a -b x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.481 |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime }+x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
1.036 |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime } = 4 x y
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.459 |
|
|
\[
{}\left (y-\cot \left (x \right ) \csc \left (x \right )\right ) y^{\prime }+\csc \left (x \right ) \left (1+y \cos \left (x \right )\right ) y = 0
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
41.793 |
|
|
\[
{}2 y y^{\prime }+2 x +x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.623 |
|
|
\[
{}2 y y^{\prime } = x y^{2}+x^{3}
\] |
[_rational, _Bernoulli] |
✓ |
1.743 |
|
|
\[
{}\left (x -2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.629 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime }+2 x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.564 |
|
|
\[
{}\left (x -2 y\right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.445 |
|
|
\[
{}\left (1+x -2 y\right ) y^{\prime } = 1+2 x -y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.478 |
|
|
\[
{}\left (1+x +2 y\right ) y^{\prime }+1-x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.986 |
|
|
\[
{}\left (1+x +2 y\right ) y^{\prime }+7+x -4 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.244 |
|
|
\[
{}2 \left (x +y\right ) y^{\prime }+x^{2}+2 y = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.327 |
|
|
\[
{}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.661 |
|
|
\[
{}\left (1-4 x -2 y\right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.121 |
|
|
\[
{}\left (6 x -2 y\right ) y^{\prime } = 2+3 x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.158 |
|
|
\[
{}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.875 |
|
|
\[
{}\left (x^{3}+2 y\right ) y^{\prime } = 3 x \left (2-x y\right )
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.489 |
|
|
\[
{}\left (\tan \left (x \right ) \sec \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 y \sin \left (x \right )\right ) = 0
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
13.462 |
|
|
\[
{}\left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime } = 2 x \,{\mathrm e}^{-2 x}-\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.206 |
|
|
\[
{}3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2} = 0
\] |
[_separable] |
✓ |
7.996 |
|
|
\[
{}3 \left (2-y\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.513 |
|
|
\[
{}\left (x -3 y\right ) y^{\prime }+4+3 x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.401 |
|
|
\[
{}\left (4-x -3 y\right ) y^{\prime }+3-x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.000 |
|
|
\[
{}\left (2+2 x +3 y\right ) y^{\prime } = 1-2 x -3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.974 |
|
|
\[
{}\left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.985 |
|
|
\[
{}\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.170 |
|
|
\[
{}\left (x +4 y\right ) y^{\prime }+4 x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.115 |
|
|
\[
{}\left (3+2 x +4 y\right ) y^{\prime } = 1+x +2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.994 |
|
|
\[
{}\left (5+2 x -4 y\right ) y^{\prime } = 3+x -2 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.107 |
|
|
\[
{}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.630 |
|
|
\[
{}4 \left (1-x -y\right ) y^{\prime }+2-x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
2.300 |
|
|
\[
{}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.197 |
|
|
\[
{}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
97.932 |
|
|
\[
{}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.579 |
|
|
\[
{}\left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.661 |
|
|
\[
{}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.648 |
|
|
\[
{}3 \left (x +2 y\right ) y^{\prime } = 1-x -2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.955 |
|
|
\[
{}\left (3-3 x +7 y\right ) y^{\prime }+7-7 x +3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.746 |
|
|
\[
{}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.949 |
|
|
\[
{}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.030 |
|
|
\[
{}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.340 |
|
|
\[
{}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.118 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
13.960 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.400 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+b x +a y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.517 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime } = b x +a y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.311 |
|