|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+\left (\frac {1}{2} x +x^{2}\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.650 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.731 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.662 |
|
|
\[
{}x y^{\prime \prime }-2 x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.283 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.582 |
|
|
\[
{}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+2 \left (-1+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.371 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.418 |
|
|
\[
{}y^{\prime } = a f \left (x \right )
\] |
[_quadrature] |
✓ |
0.179 |
|
|
\[
{}y^{\prime } = x +\sin \left (x \right )+y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.727 |
|
|
\[
{}y^{\prime } = x^{2}+3 \cosh \left (x \right )+2 y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.942 |
|
|
\[
{}y^{\prime } = a +b x +c y
\] |
[[_linear, ‘class A‘]] |
✓ |
0.836 |
|
|
\[
{}y^{\prime } = a \cos \left (b x +c \right )+k y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.622 |
|
|
\[
{}y^{\prime } = a \sin \left (b x +c \right )+k y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.629 |
|
|
\[
{}y^{\prime } = a +b \,{\mathrm e}^{k x}+c y
\] |
[[_linear, ‘class A‘]] |
✓ |
1.085 |
|
|
\[
{}y^{\prime } = x \left (x^{2}-y\right )
\] |
[_linear] |
✓ |
1.572 |
|
|
\[
{}y^{\prime } = x \left ({\mathrm e}^{-x^{2}}+a y\right )
\] |
[_linear] |
✓ |
1.364 |
|
|
\[
{}y^{\prime } = x^{2} \left (a \,x^{3}+b y\right )
\] |
[_linear] |
✓ |
2.057 |
|
|
\[
{}y^{\prime } = a \,x^{n} y
\] |
[_separable] |
✓ |
1.275 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \cos \left (x \right )+y \cos \left (x \right )
\] |
[_linear] |
✓ |
2.049 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\sin \left (x \right )}+y \cos \left (x \right )
\] |
[_linear] |
✓ |
1.902 |
|
|
\[
{}y^{\prime } = y \cot \left (x \right )
\] |
[_separable] |
✓ |
1.804 |
|
|
\[
{}y^{\prime } = 1-y \cot \left (x \right )
\] |
[_linear] |
✓ |
1.427 |
|
|
\[
{}y^{\prime } = x \csc \left (x \right )-y \cot \left (x \right )
\] |
[_linear] |
✓ |
1.869 |
|
|
\[
{}y^{\prime } = \left (2 \csc \left (2 x \right )+\cot \left (x \right )\right ) y
\] |
[_separable] |
✓ |
3.955 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )-y \cot \left (x \right )
\] |
[_linear] |
✓ |
1.891 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x} \sin \left (x \right )+y \cot \left (x \right )
\] |
[_linear] |
✓ |
2.374 |
|
|
\[
{}y^{\prime }+\csc \left (x \right )+2 y \cot \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.846 |
|
|
\[
{}y^{\prime } = 4 \csc \left (x \right ) x \sec \left (x \right )^{2}-2 y \cot \left (2 x \right )
\] |
[_linear] |
✓ |
293.542 |
|
|
\[
{}y^{\prime } = 2 \cot \left (x \right )^{2} \cos \left (2 x \right )-2 y \csc \left (2 x \right )
\] |
[_linear] |
✓ |
3.626 |
|
|
\[
{}y^{\prime } = 4 \csc \left (x \right ) x \left (\sin \left (x \right )^{3}+y\right )
\] |
[_linear] |
✓ |
12.154 |
|
|
\[
{}y^{\prime } = 4 \csc \left (x \right ) x \left (1-\tan \left (x \right )^{2}+y\right )
\] |
[_linear] |
✓ |
89.384 |
|
|
\[
{}y^{\prime } = y \sec \left (x \right )
\] |
[_separable] |
✓ |
2.090 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) = \left (1-y\right ) \sec \left (x \right )
\] |
[_linear] |
✓ |
2.173 |
|
|
\[
{}y^{\prime } = y \tan \left (x \right )
\] |
[_separable] |
✓ |
1.855 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )+y \tan \left (x \right )
\] |
[_linear] |
✓ |
1.958 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
1.862 |
|
|
\[
{}y^{\prime } = \sec \left (x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
1.799 |
|
|
\[
{}y^{\prime } = \sin \left (2 x \right )+y \tan \left (x \right )
\] |
[_linear] |
✓ |
2.039 |
|
|
\[
{}y^{\prime } = \sin \left (2 x \right )-y \tan \left (x \right )
\] |
[_linear] |
✓ |
2.006 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )+2 y \tan \left (x \right )
\] |
[_linear] |
✓ |
1.976 |
|
|
\[
{}y^{\prime } = 2+2 \sec \left (2 x \right )+2 y \tan \left (2 x \right )
\] |
[_linear] |
✓ |
9.392 |
|
|
\[
{}y^{\prime } = \csc \left (x \right )+3 y \tan \left (x \right )
\] |
[_linear] |
✓ |
2.047 |
|
|
\[
{}y^{\prime } = \left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y
\] |
[_separable] |
✓ |
1.992 |
|
|
\[
{}y^{\prime } = 6 \,{\mathrm e}^{2 x}-y \tanh \left (x \right )
\] |
[_linear] |
✓ |
2.041 |
|
|
\[
{}y^{\prime } = f \left (x \right ) f^{\prime }\left (x \right )+f^{\prime }\left (x \right ) y
\] |
[_linear] |
✓ |
0.582 |
|
|
\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y
\] |
[_linear] |
✓ |
1.055 |
|
|
\[
{}y^{\prime } = x^{2}-y^{2}
\] |
[_Riccati] |
✓ |
1.182 |
|
|
\[
{}y^{\prime }+f \left (x \right )^{2} = f^{\prime }\left (x \right )+y^{2}
\] |
[_Riccati] |
✓ |
0.999 |
|
|
\[
{}y^{\prime }+1-x = y \left (x +y\right )
\] |
[_Riccati] |
✓ |
1.545 |
|
|
\[
{}y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.629 |
|
|
\[
{}y^{\prime } = \left (x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
1.783 |
|
|
\[
{}y^{\prime } = 3-3 x +3 y+\left (x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
3.256 |
|
|
\[
{}y^{\prime } = 2 x -\left (x^{2}+1\right ) y+y^{2}
\] |
[_Riccati] |
✓ |
1.706 |
|
|
\[
{}y^{\prime } = x \left (x^{3}+2\right )-\left (2 x^{2}-y\right ) y
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
1.195 |
|
|
\[
{}y^{\prime } = 1+x \left (-x^{3}+2\right )+\left (2 x^{2}-y\right ) y
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
1.812 |
|
|
\[
{}y^{\prime } = \cos \left (x \right )-\left (\sin \left (x \right )-y\right ) y
\] |
[_Riccati] |
✓ |
3.012 |
|
|
\[
{}y^{\prime } = \cos \left (2 x \right )+\left (\sin \left (2 x \right )+y\right ) y
\] |
[_Riccati] |
✓ |
6.133 |
|
|
\[
{}y^{\prime } = f \left (x \right )+x f \left (x \right ) y+y^{2}
\] |
[_Riccati] |
✓ |
1.792 |
|
|
\[
{}y^{\prime } = \left (3+x -4 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
4.544 |
|
|
\[
{}y^{\prime } = \left (1+4 x +9 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
35.928 |
|
|
\[
{}y^{\prime } = 3 a +3 b x +3 b y^{2}
\] |
[_Riccati] |
✓ |
1.456 |
|
|
\[
{}y^{\prime } = a +b y^{2}
\] |
[_quadrature] |
✓ |
3.757 |
|
|
\[
{}y^{\prime } = a x +b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.133 |
|
|
\[
{}y^{\prime } = a +b x +c y^{2}
\] |
[_Riccati] |
✓ |
1.352 |
|
|
\[
{}y^{\prime } = a \,x^{n -1}+b \,x^{2 n}+c y^{2}
\] |
[_Riccati] |
✓ |
3.642 |
|
|
\[
{}y^{\prime } = a \,x^{2}+b y^{2}
\] |
[[_Riccati, _special]] |
✓ |
1.321 |
|
|
\[
{}y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}
\] |
[_quadrature] |
✓ |
3.605 |
|
|
\[
{}y^{\prime } = f \left (x \right )+a y+b y^{2}
\] |
[_Riccati] |
✗ |
1.418 |
|
|
\[
{}y^{\prime } = 1+a \left (x -y\right ) y
\] |
[_Riccati] |
✓ |
1.454 |
|
|
\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+a y^{2}
\] |
[_Riccati] |
✗ |
1.806 |
|
|
\[
{}y^{\prime } = x y \left (3+y\right )
\] |
[_separable] |
✓ |
2.872 |
|
|
\[
{}y^{\prime } = 1-x -x^{3}+\left (2 x^{2}+1\right ) y-x y^{2}
\] |
[_Riccati] |
✓ |
2.817 |
|
|
\[
{}y^{\prime } = x \left (2+x^{2} y-y^{2}\right )
\] |
[_Riccati] |
✓ |
1.793 |
|
|
\[
{}y^{\prime } = x +\left (1-2 x \right ) y-\left (1-x \right ) y^{2}
\] |
[_Riccati] |
✓ |
2.583 |
|
|
\[
{}y^{\prime } = a x y^{2}
\] |
[_separable] |
✓ |
1.385 |
|
|
\[
{}y^{\prime } = x^{n} \left (a +b y^{2}\right )
\] |
[_separable] |
✓ |
3.237 |
|
|
\[
{}y^{\prime } = a \,x^{m}+b \,x^{n} y^{2}
\] |
[_Riccati] |
✓ |
2.246 |
|
|
\[
{}y^{\prime } = \left (a +b y \cos \left (k x \right )\right ) y
\] |
[_Bernoulli] |
✓ |
2.249 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (2 \sec \left (x \right )^{2}-y\right )
\] |
[_linear] |
✓ |
2.626 |
|
|
\[
{}y^{\prime }+4 \csc \left (x \right ) = \left (3-\cot \left (x \right )\right ) y+y^{2} \sin \left (x \right )
\] |
[_Riccati] |
✓ |
6.687 |
|
|
\[
{}y^{\prime } = y \sec \left (x \right )+\left (\sin \left (x \right )-1\right )^{2}
\] |
[_linear] |
✓ |
3.356 |
|
|
\[
{}y^{\prime }+\tan \left (x \right ) \left (1-y^{2}\right ) = 0
\] |
[_separable] |
✓ |
2.717 |
|
|
\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{2}
\] |
[_Riccati] |
✗ |
2.540 |
|
|
\[
{}y^{\prime } = \left (a +b y+c y^{2}\right ) f \left (x \right )
\] |
[_separable] |
✓ |
3.531 |
|
|
\[
{}y^{\prime }+\left (a x +y\right ) y^{2} = 0
\] |
[_Abel] |
✗ |
0.827 |
|
|
\[
{}y^{\prime } = \left (a \,{\mathrm e}^{x}+y\right ) y^{2}
\] |
[_Abel] |
✗ |
1.369 |
|
|
\[
{}y^{\prime }+3 a \left (y+2 x \right ) y^{2} = 0
\] |
[_Abel] |
✗ |
0.860 |
|
|
\[
{}y^{\prime } = y \left (a +b y^{2}\right )
\] |
[_quadrature] |
✓ |
8.071 |
|
|
\[
{}y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3}
\] |
[_quadrature] |
✓ |
73.996 |
|
|
\[
{}y^{\prime } = x y^{3}
\] |
[_separable] |
✓ |
3.589 |
|
|
\[
{}y^{\prime }+y \left (1-x y^{2}\right ) = 0
\] |
[_Bernoulli] |
✓ |
2.944 |
|
|
\[
{}y^{\prime } = \left (a +b x y\right ) y^{2}
\] |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
2.389 |
|
|
\[
{}y^{\prime }+2 x y \left (1+a x y^{2}\right ) = 0
\] |
[_Bernoulli] |
✓ |
1.350 |
|
|
\[
{}y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y = 0
\] |
[_Bernoulli] |
✓ |
3.049 |
|
|
\[
{}y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right ) = 0
\] |
[_separable] |
✓ |
3.568 |
|
|
\[
{}y^{\prime } = \operatorname {f0} \left (x \right )+\operatorname {f1} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\operatorname {f3} \left (x \right ) y^{3}
\] |
[_Abel] |
✗ |
4.827 |
|
|
\[
{}y^{\prime } = a \,x^{\frac {n}{1-n}}+b y^{n}
\] |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
2.235 |
|
|
\[
{}y^{\prime } = f \left (x \right ) y+g \left (x \right ) y^{k}
\] |
[_Bernoulli] |
✓ |
1.768 |
|
|
\[
{}y^{\prime } = f \left (x \right )+g \left (x \right ) y+h \left (x \right ) y^{n}
\] |
[_Chini] |
✗ |
3.246 |
|
|
\[
{}y^{\prime } = \sqrt {{| y|}}
\] |
[_quadrature] |
✓ |
2.860 |
|