|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = y^{2}-a^{2}+a \lambda \sinh \left (\lambda x \right )-a^{2} \sinh \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
11.519 |
|
|
\[
{}y^{\prime } = y^{2}+a \sinh \left (\beta x \right ) y+a b \sinh \left (\beta x \right )-b^{2}
\] |
[_Riccati] |
✓ |
4.475 |
|
|
\[
{}y^{\prime } = y^{2}+a x \sinh \left (b x \right )^{m} y+a \sinh \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
8.675 |
|
|
\[
{}y^{\prime } = \lambda \sinh \left (\lambda x \right ) y^{2}-\lambda \sinh \left (\lambda x \right )^{3}
\] |
[_Riccati] |
✓ |
8.851 |
|
|
\[
{}y^{\prime } = \left (a \sinh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}-a \sinh \left (\lambda x \right )^{2}+\lambda -a
\] |
[_Riccati] |
✓ |
29.718 |
|
|
\[
{}\left (a \sinh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \sinh \left (\mu x \right ) y-d^{2}+c d \sinh \left (\mu x \right )
\] |
[_Riccati] |
✗ |
116.998 |
|
|
\[
{}\left (a \sinh \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \sinh \left (\lambda x \right ) = 0
\] |
[_Riccati] |
✓ |
5.564 |
|
|
\[
{}y^{\prime } = \alpha y^{2}+\beta +\gamma \cosh \left (x \right )
\] |
[_Riccati] |
✓ |
2.671 |
|
|
\[
{}y^{\prime } = y^{2}+a \cosh \left (\beta x \right ) y+a b \cosh \left (\beta x \right )-b^{2}
\] |
[_Riccati] |
✓ |
4.178 |
|
|
\[
{}y^{\prime } = y^{2}+a x \cosh \left (b x \right )^{m} y+a \cosh \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
7.595 |
|
|
\[
{}y^{\prime } = \left (a \cosh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
27.774 |
|
|
\[
{}2 y^{\prime } = \left (a -\lambda +a \cosh \left (\lambda x \right )\right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right )
\] |
[_Riccati] |
✓ |
27.400 |
|
|
\[
{}y^{\prime } = y^{2}-\lambda ^{2}+a \cosh \left (\lambda x \right )^{n} \sinh \left (\lambda x \right )^{-n -4}
\] |
[_Riccati] |
✗ |
29.810 |
|
|
\[
{}y^{\prime } = a \sinh \left (\lambda x \right ) y^{2}+b \sinh \left (\lambda x \right ) \cosh \left (\lambda x \right )^{n}
\] |
[_Riccati] |
✓ |
11.479 |
|
|
\[
{}y^{\prime } = a \cosh \left (\lambda x \right ) y^{2}+b \cosh \left (\lambda x \right ) \sinh \left (\lambda x \right )^{n}
\] |
[_Riccati] |
✓ |
11.573 |
|
|
\[
{}\left (a \cosh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cosh \left (\mu x \right ) y-d^{2}+c d \cosh \left (\mu x \right )
\] |
[_Riccati] |
✗ |
174.512 |
|
|
\[
{}\left (a \cosh \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \cosh \left (\lambda x \right ) = 0
\] |
[_Riccati] |
✓ |
5.173 |
|
|
\[
{}y^{\prime } = y^{2}+a \lambda -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
5.052 |
|
|
\[
{}y^{\prime } = y^{2}+3 a \lambda -\lambda ^{2}-a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
4.910 |
|
|
\[
{}y^{\prime } = y^{2}+a x \tanh \left (b x \right )^{m} y+a \tanh \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
6.082 |
|
|
\[
{}\left (a \tanh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \tanh \left (\mu x \right ) y-d^{2}+c d \tanh \left (\mu x \right )
\] |
[_Riccati] |
✗ |
293.752 |
|
|
\[
{}y^{\prime } = y^{2}+a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
4.906 |
|
|
\[
{}y^{\prime } = y^{2}-\lambda ^{2}+3 a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
4.438 |
|
|
\[
{}y^{\prime } = y^{2}+a x \coth \left (b x \right )^{m} y+a \coth \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
6.733 |
|
|
\[
{}\left (a \coth \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \coth \left (\mu x \right ) y-d^{2}+c d \coth \left (\mu x \right )
\] |
[_Riccati] |
✗ |
327.952 |
|
|
\[
{}y^{\prime } = y^{2}-2 \lambda ^{2} \tanh \left (\lambda x \right )^{2}-2 \lambda ^{2} \coth \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
19.472 |
|
|
\[
{}y^{\prime } = y^{2}+a \lambda +b \lambda -2 a b -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}-b \left (b +\lambda \right ) \coth \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
19.355 |
|
|
\[
{}y^{\prime } = a \ln \left (x \right )^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{2 m} \ln \left (x \right )^{n}
\] |
[_Riccati] |
✗ |
7.409 |
|
|
\[
{}x y^{\prime } = y^{2} a +b \ln \left (x \right )+c
\] |
[_Riccati] |
✓ |
2.133 |
|
|
\[
{}x y^{\prime } = y^{2} a +b \ln \left (x \right )^{k}+c \ln \left (x \right )^{2 k +2}
\] |
[_Riccati] |
✓ |
35.891 |
|
|
\[
{}x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2}+a
\] |
[_Riccati] |
✗ |
2.392 |
|
|
\[
{}x y^{\prime } = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2 k}+a k \ln \left (\beta x \right )^{k -1}
\] |
[_Riccati] |
✗ |
4.844 |
|
|
\[
{}x y^{\prime } = a \,x^{n} y^{2}+b -a \,b^{2} x^{n} \ln \left (x \right )^{2}
\] |
[_Riccati] |
✗ |
3.502 |
|
|
\[
{}x^{2} y^{\prime } = y^{2} x^{2}+a \ln \left (x \right )^{2}+b \ln \left (x \right )+c
\] |
[_Riccati] |
✓ |
7.441 |
|
|
\[
{}x^{2} y^{\prime } = y^{2} x^{2}+a \left (b \ln \left (x \right )+c \right )^{n}+\frac {1}{4}
\] |
[_Riccati] |
✗ |
3.359 |
|
|
\[
{}x^{2} \ln \left (a x \right ) \left (y^{\prime }-y^{2}\right ) = 1
\] |
[_Riccati] |
✓ |
1.599 |
|
|
\[
{}y^{\prime } = y^{2}+a \ln \left (\beta x \right ) y-a b \ln \left (\beta x \right )-b^{2}
\] |
[_Riccati] |
✓ |
2.339 |
|
|
\[
{}y^{\prime } = y^{2}+a x \ln \left (b x \right )^{m} y+a \ln \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
2.276 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}-a b \,x^{n +1} \ln \left (x \right ) y+b \ln \left (x \right )+b
\] |
[_Riccati] |
✓ |
3.468 |
|
|
\[
{}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{n +1} \ln \left (x \right )^{m} y-a \ln \left (x \right )^{m}
\] |
[_Riccati] |
✓ |
3.587 |
|
|
\[
{}y^{\prime } = a \ln \left (x \right )^{n} y-a b x \ln \left (x \right )^{n +1} y+b \ln \left (x \right )+b
\] |
[_linear] |
✓ |
2.276 |
|
|
\[
{}y^{\prime } = a \ln \left (x \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
5.716 |
|
|
\[
{}y^{\prime } = a \ln \left (x \right )^{n} y^{2}+b \ln \left (x \right )^{m} y+b c \ln \left (x \right )^{m}-a \,c^{2} \ln \left (x \right )^{n}
\] |
[_Riccati] |
✗ |
5.505 |
|
|
\[
{}x y^{\prime } = \left (a y+b \ln \left (x \right )\right )^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
1.562 |
|
|
\[
{}x y^{\prime } = a \ln \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \ln \left (\lambda x \right )^{m}
\] |
[_Riccati] |
✓ |
38.800 |
|
|
\[
{}x y^{\prime } = a \,x^{n} \left (y+b \ln \left (x \right )\right )^{2}-b
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.795 |
|
|
\[
{}x y^{\prime } = a \,x^{2 n} \ln \left (x \right ) y^{2}+\left (b \,x^{n} \ln \left (x \right )-n \right ) y+c \ln \left (x \right )
\] |
[_Riccati] |
✓ |
4.676 |
|
|
\[
{}x^{2} y^{\prime } = a^{2} x^{2} y^{2}-x y+b^{2} \ln \left (x \right )^{n}
\] |
[_Riccati] |
✓ |
3.154 |
|
|
\[
{}\left (a \ln \left (x \right )+b \right ) y^{\prime } = y^{2}+c \ln \left (x \right )^{n} y-\lambda ^{2}+\lambda c \ln \left (x \right )^{n}
\] |
[_Riccati] |
✗ |
38.732 |
|
|
\[
{}\left (a \ln \left (x \right )+b \right ) y^{\prime } = \ln \left (x \right )^{n} y^{2}+c y-\lambda ^{2} \ln \left (x \right )^{n}+\lambda c
\] |
[_Riccati] |
✗ |
44.703 |
|
|
\[
{}y^{\prime } = \alpha y^{2}+\beta +\gamma \sin \left (\lambda x \right )
\] |
[_Riccati] |
✓ |
3.324 |
|
|
\[
{}y^{\prime } = y^{2}-a^{2}+a \lambda \sin \left (\lambda x \right )+a^{2} \sin \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
7.693 |
|
|
\[
{}y^{\prime } = y^{2}+\lambda ^{2}+c \sin \left (\lambda x +a \right )^{n} \sin \left (\lambda x +b \right )^{-n -4}
\] |
[_Riccati] |
✗ |
161.015 |
|
|
\[
{}y^{\prime } = y^{2}+a \sin \left (\beta x \right ) y+a b \sin \left (\beta x \right )-b^{2}
\] |
[_Riccati] |
✓ |
4.606 |
|
|
\[
{}y^{\prime } = y^{2}+a \sin \left (b x \right )^{m} y+a \sin \left (b x \right )^{m}
\] |
[_Riccati] |
✗ |
16.779 |
|
|
\[
{}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+\lambda \sin \left (\lambda x \right )^{3}
\] |
[_Riccati] |
✓ |
8.116 |
|
|
\[
{}2 y^{\prime } = \left (\lambda +a -a \sin \left (\lambda x \right )\right ) y^{2}+\lambda -a -a \sin \left (\lambda x \right )
\] |
[_Riccati] |
✓ |
75.004 |
|
|
\[
{}y^{\prime } = \left (\lambda +a \sin \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \sin \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
33.953 |
|
|
\[
{}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \sin \left (x \right )^{m} y-a \sin \left (x \right )^{m}
\] |
[_Riccati] |
✓ |
21.405 |
|
|
\[
{}y^{\prime } = a \sin \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
66.997 |
|
|
\[
{}x y^{\prime } = a \sin \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \sin \left (\lambda x \right )^{m}
\] |
[_Riccati] |
✓ |
22.758 |
|
|
\[
{}\left (a \sin \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \sin \left (\mu x \right ) y-d^{2}+c d \sin \left (\mu x \right )
\] |
[_Riccati] |
✗ |
123.118 |
|
|
\[
{}\left (a \sin \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \sin \left (\lambda x \right ) = 0
\] |
[_Riccati] |
✓ |
5.676 |
|
|
\[
{}y^{\prime } = \alpha y^{2}+\beta +\gamma \cos \left (\lambda x \right )
\] |
[_Riccati] |
✓ |
2.973 |
|
|
\[
{}y^{\prime } = y^{2}-a^{2}+a \lambda \cos \left (\lambda x \right )+a^{2} \cos \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
6.419 |
|
|
\[
{}y^{\prime } = y^{2}+\lambda ^{2}+c \cos \left (\lambda x +a \right )^{n} \cos \left (\lambda x +b \right )^{-n -4}
\] |
[_Riccati] |
✗ |
162.096 |
|
|
\[
{}y^{\prime } = y^{2}+a \cos \left (\beta x \right ) y+a b \cos \left (\beta x \right )-b^{2}
\] |
[_Riccati] |
✓ |
4.633 |
|
|
\[
{}y^{\prime } = y^{2}+a \cos \left (b x \right )^{m} y+a \cos \left (b x \right )^{m}
\] |
[_Riccati] |
✗ |
14.886 |
|
|
\[
{}y^{\prime } = \lambda \cos \left (\lambda x \right ) y^{2}+\lambda \cos \left (\lambda x \right )^{3}
\] |
[_Riccati] |
✓ |
18.010 |
|
|
\[
{}2 y^{\prime } = \left (\lambda +a -a \cos \left (\lambda x \right )\right ) y^{2}+\lambda -a -a \cos \left (\lambda x \right )
\] |
[_Riccati] |
✓ |
43.472 |
|
|
\[
{}y^{\prime } = \left (\lambda +a \cos \left (\lambda x \right )^{2}\right ) y^{2}+\lambda -a +a \cos \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
29.284 |
|
|
\[
{}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \cos \left (x \right )^{m} y-a \cos \left (x \right )^{m}
\] |
[_Riccati] |
✓ |
18.194 |
|
|
\[
{}y^{\prime } = a \cos \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
40.821 |
|
|
\[
{}x y^{\prime } = a \cos \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cos \left (\lambda x \right )^{m}
\] |
[_Riccati] |
✓ |
50.393 |
|
|
\[
{}\left (a \cos \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cos \left (\mu x \right ) y-d^{2}+c d \cos \left (\mu x \right )
\] |
[_Riccati] |
✗ |
120.270 |
|
|
\[
{}\left (a \cos \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )-a \,\lambda ^{2} \cos \left (\lambda x \right ) = 0
\] |
[_Riccati] |
✓ |
5.286 |
|
|
\[
{}y^{\prime } = y^{2}+a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
5.816 |
|
|
\[
{}y^{\prime } = y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \tan \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
6.168 |
|
|
\[
{}y^{\prime } = y^{2} a +b \tan \left (x \right ) y+c
\] |
[_Riccati] |
✓ |
5.289 |
|
|
\[
{}y^{\prime } = y^{2} a +2 a b \tan \left (x \right ) y+b \left (a b -1\right ) \tan \left (x \right )^{2}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
3.293 |
|
|
\[
{}y^{\prime } = y^{2}+a \tan \left (\beta x \right ) y+a b \tan \left (\beta x \right )-b^{2}
\] |
[_Riccati] |
✓ |
5.002 |
|
|
\[
{}y^{\prime } = y^{2}+a x \tan \left (b x \right )^{m} y+a \tan \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
6.261 |
|
|
\[
{}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \tan \left (x \right )^{m} y-a \tan \left (x \right )^{m}
\] |
[_Riccati] |
✓ |
13.619 |
|
|
\[
{}y^{\prime } = a \tan \left (\lambda x \right )^{n} y^{2}-a \,b^{2} \tan \left (\lambda x \right )^{2+n}+b \lambda \tan \left (\lambda x \right )^{2}+b \lambda
\] |
[_Riccati] |
✓ |
34.124 |
|
|
\[
{}y^{\prime } = a \tan \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
148.893 |
|
|
\[
{}x y^{\prime } = a \tan \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \tan \left (\lambda x \right )^{m}
\] |
[_Riccati] |
✓ |
59.906 |
|
|
\[
{}\left (a \tan \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+k \tan \left (\mu x \right ) y-d^{2}+k d \tan \left (\mu x \right )
\] |
[_Riccati] |
✗ |
224.790 |
|
|
\[
{}y^{\prime } = y^{2}+a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
6.014 |
|
|
\[
{}y^{\prime } = y^{2}+\lambda ^{2}+3 a \lambda +a \left (\lambda -a \right ) \cot \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
5.637 |
|
|
\[
{}y^{\prime } = y^{2}-2 a b \cot \left (a x \right ) y+b^{2}-a^{2}
\] |
[_Riccati] |
✓ |
7.523 |
|
|
\[
{}y^{\prime } = y^{2}+a \cot \left (\beta x \right ) y+a b \cot \left (\beta x \right )-b^{2}
\] |
[_Riccati] |
✓ |
6.238 |
|
|
\[
{}y^{\prime } = y^{2}+a x \cot \left (b x \right )^{m} y+a \cot \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
6.862 |
|
|
\[
{}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} \cot \left (x \right )^{m} y-a \cot \left (x \right )^{m}
\] |
[_Riccati] |
✓ |
14.811 |
|
|
\[
{}y^{\prime } = a \cot \left (\lambda x +\mu \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✗ |
182.798 |
|
|
\[
{}x y^{\prime } = a \cot \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \cot \left (\lambda x \right )^{m}
\] |
[_Riccati] |
✓ |
61.205 |
|
|
\[
{}\left (a \cot \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cot \left (\mu x \right ) y-d^{2}+c d \cot \left (\mu x \right )
\] |
[_Riccati] |
✗ |
212.609 |
|
|
\[
{}y^{\prime } = y^{2}+\lambda ^{2}+c \sin \left (\lambda x \right )^{n} \cos \left (\lambda x \right )^{-n -4}
\] |
[_Riccati] |
✗ |
27.997 |
|
|
\[
{}y^{\prime } = a \sin \left (\lambda x \right ) y^{2}+b \sin \left (\lambda x \right ) \cos \left (\lambda x \right )^{n}
\] |
[_Riccati] |
✓ |
12.223 |
|
|
\[
{}y^{\prime } = \lambda \sin \left (\lambda x \right ) y^{2}+a \cos \left (\lambda x \right )^{n} y-a \cos \left (\lambda x \right )^{n -1}
\] |
[_Riccati] |
✗ |
68.506 |
|
|
\[
{}y^{\prime } = a \cos \left (\lambda x \right ) y^{2}+b \cos \left (\lambda x \right ) \sin \left (\lambda x \right )^{n}
\] |
[_Riccati] |
✓ |
13.525 |
|