|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } \sqrt {x^{4}+x^{2}+1} = \sqrt {1+y^{2}+y^{4}}
\] |
[_separable] |
✓ |
2.904 |
|
|
\[
{}y^{\prime } \sqrt {X} = 0
\] |
[_quadrature] |
✓ |
0.418 |
|
|
\[
{}y^{\prime } \sqrt {X}+\sqrt {Y} = 0
\] |
[_quadrature] |
✓ |
0.407 |
|
|
\[
{}y^{\prime } \sqrt {X} = \sqrt {Y}
\] |
[_quadrature] |
✓ |
0.408 |
|
|
\[
{}y^{\prime } \left (x^{3}+1\right )^{{2}/{3}}+\left (y^{3}+1\right )^{{2}/{3}} = 0
\] |
[_separable] |
✓ |
1.868 |
|
|
\[
{}y^{\prime } \left (4 x^{3}+\operatorname {a1} x +\operatorname {a0} \right )^{{2}/{3}}+\left (\operatorname {a0} +\operatorname {a1} y+4 y^{3}\right )^{{2}/{3}} = 0
\] |
[_separable] |
✓ |
2.333 |
|
|
\[
{}X^{{2}/{3}} y^{\prime } = Y^{{2}/{3}}
\] |
[_quadrature] |
✓ |
0.544 |
|
|
\[
{}y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right ) = y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right )
\] |
[_Bernoulli] |
✓ |
18.404 |
|
|
\[
{}\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime } = \tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y
\] |
[_separable] |
✓ |
7.220 |
|
|
\[
{}\left (-\sin \left (x \right )+1\right ) y^{\prime }+y \cos \left (x \right ) = 0
\] |
[_separable] |
✓ |
2.752 |
|
|
\[
{}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = 0
\] |
[_separable] |
✓ |
3.184 |
|
|
\[
{}\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )+\operatorname {a1} y \sin \left (2 x \right ) = 0
\] |
[_linear] |
✓ |
12.011 |
|
|
\[
{}\left (-{\mathrm e}^{x}+x \right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (1-{\mathrm e}^{x}\right ) y = 0
\] |
[_linear] |
✓ |
1.597 |
|
|
\[
{}y^{\prime } x \ln \left (x \right ) = a x \left (\ln \left (x \right )+1\right )-y
\] |
[_linear] |
✓ |
1.260 |
|
|
\[
{}y^{\prime } y+x = 0
\] |
[_separable] |
✓ |
2.845 |
|
|
\[
{}y^{\prime } y+x \,{\mathrm e}^{x^{2}} = 0
\] |
[_separable] |
✓ |
1.309 |
|
|
\[
{}y^{\prime } y+x^{3}+y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.661 |
|
|
\[
{}y^{\prime } y+a x +b y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.948 |
|
|
\[
{}y^{\prime } y+x \,{\mathrm e}^{-x} \left (y+1\right ) = 0
\] |
[_separable] |
✓ |
1.975 |
|
|
\[
{}y^{\prime } y+f \left (x \right ) = g \left (x \right ) y
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.980 |
|
|
\[
{}y^{\prime } y+4 \left (x +1\right ) x +y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.888 |
|
|
\[
{}y^{\prime } y = a x +b y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
1.427 |
|
|
\[
{}y^{\prime } y = b \cos \left (x +c \right )+y^{2} a
\] |
[_Bernoulli] |
✓ |
2.908 |
|
|
\[
{}y^{\prime } y = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}
\] |
[_quadrature] |
✓ |
3.483 |
|
|
\[
{}y^{\prime } y = a x +b x y^{2}
\] |
[_separable] |
✓ |
1.920 |
|
|
\[
{}y^{\prime } y = \csc \left (x \right )^{2}-y^{2} \cot \left (x \right )
\] |
[_Bernoulli] |
✓ |
13.714 |
|
|
\[
{}y^{\prime } y = \sqrt {y^{2}+a^{2}}
\] |
[_quadrature] |
✓ |
6.200 |
|
|
\[
{}y^{\prime } y = \sqrt {y^{2}-a^{2}}
\] |
[_quadrature] |
✓ |
5.960 |
|
|
\[
{}y^{\prime } y+x +f \left (y^{2}+x^{2}\right ) g \left (x \right ) = 0
\] |
[NONE] |
✗ |
2.837 |
|
|
\[
{}\left (y+1\right ) y^{\prime } = x +y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.071 |
|
|
\[
{}\left (y+1\right ) y^{\prime } = x^{2} \left (1-y\right )
\] |
[_separable] |
✓ |
1.273 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.727 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.506 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.625 |
|
|
\[
{}\left (x +y\right ) y^{\prime } = x -y
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.635 |
|
|
\[
{}1-y^{\prime } = x +y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.997 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = y \left (1+2 x y\right )
\] |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.476 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+\tan \left (y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.139 |
|
|
\[
{}\left (x -y\right ) y^{\prime } = \left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.987 |
|
|
\[
{}\left (x +y+1\right ) y^{\prime }+1+4 x +3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.802 |
|
|
\[
{}\left (2+x +y\right ) y^{\prime } = 1-x -y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.457 |
|
|
\[
{}\left (3-x -y\right ) y^{\prime } = 1+x -3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.911 |
|
|
\[
{}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.914 |
|
|
\[
{}\left (2 x +y\right ) y^{\prime }+x -2 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.690 |
|
|
\[
{}\left (2+2 x -y\right ) y^{\prime }+3+6 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.370 |
|
|
\[
{}\left (2 x -y+3\right ) y^{\prime }+2 = 0
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.355 |
|
|
\[
{}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.212 |
|
|
\[
{}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.568 |
|
|
\[
{}\left (1-3 x +y\right ) y^{\prime } = 2 x -2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.142 |
|
|
\[
{}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.608 |
|
|
\[
{}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.364 |
|
|
\[
{}\left (6-4 x -y\right ) y^{\prime } = 2 x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.621 |
|
|
\[
{}\left (1+5 x -y\right ) y^{\prime }+5+x -5 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.752 |
|
|
\[
{}\left (a +b x +y\right ) y^{\prime }+a -b x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.777 |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime }+x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
0.951 |
|
|
\[
{}\left (x^{2}-y\right ) y^{\prime } = 4 x y
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.026 |
|
|
\[
{}\left (y-\cot \left (x \right ) \csc \left (x \right )\right ) y^{\prime }+\csc \left (x \right ) \left (1+y \cos \left (x \right )\right ) y = 0
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
39.678 |
|
|
\[
{}2 y^{\prime } y+2 x +x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.983 |
|
|
\[
{}2 y^{\prime } y = x y^{2}+x^{3}
\] |
[_rational, _Bernoulli] |
✓ |
1.391 |
|
|
\[
{}\left (x -2 y\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.656 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime }+2 x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.715 |
|
|
\[
{}\left (x -2 y\right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.291 |
|
|
\[
{}\left (1+x -2 y\right ) y^{\prime } = 1+2 x -y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.953 |
|
|
\[
{}\left (1+x +2 y\right ) y^{\prime }+1-x -2 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.317 |
|
|
\[
{}\left (1+x +2 y\right ) y^{\prime }+7+x -4 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.336 |
|
|
\[
{}2 \left (x +y\right ) y^{\prime }+x^{2}+2 y = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.120 |
|
|
\[
{}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.598 |
|
|
\[
{}\left (1-4 x -2 y\right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.471 |
|
|
\[
{}\left (6 x -2 y\right ) y^{\prime } = 2+3 x -y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.404 |
|
|
\[
{}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.189 |
|
|
\[
{}\left (x^{3}+2 y\right ) y^{\prime } = 3 x \left (2-x y\right )
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.296 |
|
|
\[
{}\left (\tan \left (x \right ) \sec \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 y \sin \left (x \right )\right ) = 0
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
10.423 |
|
|
\[
{}\left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime } = 2 x \,{\mathrm e}^{-2 x}-\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.592 |
|
|
\[
{}3 y^{\prime } y+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2} = 0
\] |
[_separable] |
✓ |
6.485 |
|
|
\[
{}3 \left (2-y\right ) y^{\prime }+x y = 0
\] |
[_separable] |
✓ |
1.214 |
|
|
\[
{}\left (x -3 y\right ) y^{\prime }+4+3 x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.949 |
|
|
\[
{}\left (4-x -3 y\right ) y^{\prime }+3-x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.332 |
|
|
\[
{}\left (2+2 x +3 y\right ) y^{\prime } = 1-2 x -3 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.320 |
|
|
\[
{}\left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.325 |
|
|
\[
{}\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.531 |
|
|
\[
{}\left (4 y+x \right ) y^{\prime }+4 x -y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.237 |
|
|
\[
{}\left (3+2 x +4 y\right ) y^{\prime } = 1+x +2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.351 |
|
|
\[
{}\left (5+2 x -4 y\right ) y^{\prime } = 3+x -2 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.648 |
|
|
\[
{}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.753 |
|
|
\[
{}4 \left (1-x -y\right ) y^{\prime }+2-x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
1.816 |
|
|
\[
{}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.635 |
|
|
\[
{}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
61.956 |
|
|
\[
{}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.119 |
|
|
\[
{}\left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.758 |
|
|
\[
{}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.266 |
|
|
\[
{}3 \left (x +2 y\right ) y^{\prime } = 1-x -2 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.282 |
|
|
\[
{}\left (3-3 x +7 y\right ) y^{\prime }+7-7 x +3 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.420 |
|
|
\[
{}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.837 |
|
|
\[
{}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.839 |
|
|
\[
{}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.164 |
|
|
\[
{}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.000 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
11.329 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.711 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime }+b x +a y = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.369 |
|
|
\[
{}\left (a x +b y\right ) y^{\prime } = b x +a y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.207 |
|