|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x \left (a \,x^{k}+b \right ) y^{\prime } = \alpha \,x^{n} y^{2}+\left (\beta -a n \,x^{k}\right ) y+\gamma \,x^{-n}
\] |
[_rational, _Riccati] |
✓ |
70.162 |
|
|
\[
{}x^{2} \left (a \,x^{n}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (p \,x^{n}+q \right ) x y+r \,x^{n}+s = 0
\] |
[_rational, _Riccati] |
✓ |
35.956 |
|
|
\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = c y^{2}-b \,x^{m -1} y+a \,x^{n -2}
\] |
[_rational, _Riccati] |
✗ |
116.549 |
|
|
\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = a \,x^{n -2} y^{2}+b \,x^{m -1} y+c
\] |
[_rational, _Riccati] |
✗ |
112.555 |
|
|
\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) y^{\prime } = \alpha \,x^{k} y^{2}+\beta \,x^{s} y-\alpha \,\lambda ^{2} x^{k}+\beta \lambda \,x^{s}
\] |
[_rational, _Riccati] |
✗ |
158.516 |
|
|
\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) \left (-y+y^{\prime } x \right )+s \,x^{k} \left (y^{2}-\lambda \,x^{2}\right ) = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
81.275 |
|
|
\[
{}y^{\prime } = a y^{2}+b \,{\mathrm e}^{\lambda x}
\] |
[_Riccati] |
✓ |
1.382 |
|
|
\[
{}y^{\prime } = y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x}
\] |
[_Riccati] |
✓ |
1.802 |
|
|
\[
{}y^{\prime } = \sigma y^{2}+a +b \,{\mathrm e}^{\lambda x}+c \,{\mathrm e}^{2 \lambda x}
\] |
[_Riccati] |
✗ |
105.916 |
|
|
\[
{}y^{\prime } = \sigma y^{2}+a y+b \,{\mathrm e}^{x}+c
\] |
[_Riccati] |
✓ |
1.923 |
|
|
\[
{}y^{\prime } = y^{2}+b y+a \left (\lambda -b \right ) {\mathrm e}^{\lambda x}-a^{2} {\mathrm e}^{2 \lambda x}
\] |
[_Riccati] |
✓ |
2.292 |
|
|
\[
{}y^{\prime } = y^{2}+a \,{\mathrm e}^{\lambda x} y-a b \,{\mathrm e}^{\lambda x}-b^{2}
\] |
[_Riccati] |
✗ |
23.132 |
|
|
\[
{}y^{\prime } = y^{2}+a \,{\mathrm e}^{2 \lambda x} \left ({\mathrm e}^{\lambda x}+b \right )^{n}-\frac {\lambda ^{2}}{4}
\] |
[_Riccati] |
✗ |
362.948 |
|
|
\[
{}y^{\prime } = y^{2}+a \,{\mathrm e}^{8 \lambda x}+b \,{\mathrm e}^{6 \lambda x}+c \,{\mathrm e}^{4 \lambda x}-\lambda ^{2}
\] |
[_Riccati] |
✓ |
7.982 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{k x} y^{2}+b \,{\mathrm e}^{s x}
\] |
[_Riccati] |
✓ |
2.290 |
|
|
\[
{}y^{\prime } = b \,{\mathrm e}^{\mu x} y^{2}+a \lambda \,{\mathrm e}^{\lambda x}-a^{2} b \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x}
\] |
[_Riccati] |
✗ |
2.595 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b y+c \,{\mathrm e}^{-\lambda x}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
3.398 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{\mu x} y^{2}+\lambda y-a \,b^{2} {\mathrm e}^{\left (\mu +2 \lambda \right ) x}
\] |
[_Riccati] |
✓ |
2.153 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y+a \lambda \,{\mathrm e}^{\left (\mu -\lambda \right ) x}
\] |
[_Riccati] |
✓ |
3.073 |
|
|
\[
{}y^{\prime } = -\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,{\mathrm e}^{\mu x} y-a \,{\mathrm e}^{\left (\mu -\lambda \right ) x}
\] |
[_Riccati] |
✓ |
3.008 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{\mu x} y^{2}+a b \,{\mathrm e}^{\left (\lambda +\mu \right ) x} y-b \lambda \,{\mathrm e}^{\lambda x}
\] |
[_Riccati] |
✗ |
347.442 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{s x}+d \,{\mathrm e}^{-k x}
\] |
[_Riccati] |
✓ |
3.329 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{\left (\mu +2 \lambda \right ) x} y^{2}+\left (b \,{\mathrm e}^{\left (\lambda +\mu \right ) x}-\lambda \right ) y+c \,{\mathrm e}^{\mu x}
\] |
[_Riccati] |
✓ |
2.931 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{k x} y^{2}+b y+c \,{\mathrm e}^{k n x}+d \,{\mathrm e}^{k \left (2 n +1\right ) x}
\] |
[_Riccati] |
✗ |
2.993 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\mu x} \left (y-b \,{\mathrm e}^{\lambda x}\right )^{2}+b \lambda \,{\mathrm e}^{\lambda x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.377 |
|
|
\[
{}\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) y^{\prime } = y^{2}+k \,{\mathrm e}^{\nu x} y-m^{2}+k m \,{\mathrm e}^{\nu x}
\] |
[_Riccati] |
✗ |
60.825 |
|
|
\[
{}\left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+c \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} {\mathrm e}^{\lambda x}+b \,\mu ^{2} {\mathrm e}^{\mu x} = 0
\] |
[_Riccati] |
✓ |
4.428 |
|
|
\[
{}y^{\prime } = y^{2}+a x \,{\mathrm e}^{\lambda x} y+a \,{\mathrm e}^{\lambda x}
\] |
[_Riccati] |
✓ |
2.283 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b \,{\mathrm e}^{-\lambda x}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
1.947 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}+b n \,x^{n -1}-a \,b^{2} {\mathrm e}^{\lambda x} x^{2 n}
\] |
[_Riccati] |
✗ |
3.584 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{\lambda x} y^{2}+a \,x^{n} y+a \lambda \,x^{n} {\mathrm e}^{-\lambda x}
\] |
[_Riccati] |
✗ |
2.747 |
|
|
\[
{}y^{\prime } = -\lambda \,{\mathrm e}^{\lambda x} y^{2}+a \,x^{n} {\mathrm e}^{\lambda x} y-a \,x^{n}
\] |
[_Riccati] |
✓ |
2.927 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{\lambda x} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b n \,x^{n -1}
\] |
[_Riccati] |
✓ |
3.898 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+b \lambda \,{\mathrm e}^{\lambda x}-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x}
\] |
[_Riccati] |
✗ |
3.519 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+\lambda y-a \,b^{2} x^{n} {\mathrm e}^{2 \lambda x}
\] |
[_Riccati] |
✓ |
2.612 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}-a b \,x^{n} {\mathrm e}^{\lambda x} y+b \lambda \,{\mathrm e}^{\lambda x}
\] |
[_Riccati] |
✗ |
3.334 |
|
|
\[
{}y^{\prime } = -\left (k +1\right ) x^{k} y^{2}+a \,x^{k +1} {\mathrm e}^{\lambda x} y-a \,{\mathrm e}^{\lambda x}
\] |
[_Riccati] |
✓ |
3.511 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}-a \,x^{n} \left (b \,{\mathrm e}^{\lambda x}+c \right ) y+c \,x^{n}
\] |
[_Riccati] |
✗ |
4.129 |
|
|
\[
{}y^{\prime } = a \,x^{n} {\mathrm e}^{2 \lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-\lambda \right ) y+c \,x^{n}
\] |
[_Riccati] |
✓ |
4.846 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{\lambda x} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
3.594 |
|
|
\[
{}y^{\prime } x = a \,{\mathrm e}^{\lambda x} y^{2}+k y+a \,b^{2} x^{2 k} {\mathrm e}^{\lambda x}
\] |
[_Riccati] |
✓ |
2.979 |
|
|
\[
{}y^{\prime } x = a \,x^{2 n} {\mathrm e}^{\lambda x} y^{2}+\left (b \,x^{n} {\mathrm e}^{\lambda x}-n \right ) y+c \,{\mathrm e}^{\lambda x}
\] |
[_Riccati] |
✗ |
5.753 |
|
|
\[
{}y^{\prime } = y^{2}+2 a \lambda x \,{\mathrm e}^{\lambda \,x^{2}}-a^{2} {\mathrm e}^{2 \lambda \,x^{2}}
\] |
[_Riccati] |
✗ |
1.861 |
|
|
\[
{}y^{\prime } = a \,{\mathrm e}^{-\lambda \,x^{2}} y^{2}+\lambda x y+a \,b^{2}
\] |
[_Riccati] |
✓ |
1.963 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+\lambda x y+a \,b^{2} x^{n} {\mathrm e}^{\lambda \,x^{2}}
\] |
[_Riccati] |
✓ |
3.133 |
|
|
\[
{}x^{4} \left (y^{\prime }-y^{2}\right ) = a +b \,{\mathrm e}^{\frac {k}{x}}+c \,{\mathrm e}^{\frac {2 k}{x}}
\] |
[_Riccati] |
✗ |
130.549 |
|
|
\[
{}y^{\prime } = y^{2}-a^{2}+a \lambda \sinh \left (\lambda x \right )-a^{2} \sinh \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
9.430 |
|
|
\[
{}y^{\prime } = y^{2}+a \sinh \left (\beta x \right ) y+a b \sinh \left (\beta x \right )-b^{2}
\] |
[_Riccati] |
✓ |
3.522 |
|
|
\[
{}y^{\prime } = y^{2}+a x \sinh \left (b x \right )^{m} y+a \sinh \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
8.106 |
|
|
\[
{}y^{\prime } = \lambda \sinh \left (\lambda x \right ) y^{2}-\lambda \sinh \left (\lambda x \right )^{3}
\] |
[_Riccati] |
✓ |
5.161 |
|
|
\[
{}y^{\prime } = \left (a \sinh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}-a \sinh \left (\lambda x \right )^{2}+\lambda -a
\] |
[_Riccati] |
✓ |
15.591 |
|
|
\[
{}\left (a \sinh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \sinh \left (\mu x \right ) y-d^{2}+c d \sinh \left (\mu x \right )
\] |
[_Riccati] |
✗ |
101.574 |
|
|
\[
{}\left (a \sinh \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \sinh \left (\lambda x \right ) = 0
\] |
[_Riccati] |
✓ |
4.954 |
|
|
\[
{}y^{\prime } = \alpha y^{2}+\beta +\gamma \cosh \left (x \right )
\] |
[_Riccati] |
✓ |
2.189 |
|
|
\[
{}y^{\prime } = y^{2}+a \cosh \left (\beta x \right ) y+a b \cosh \left (\beta x \right )-b^{2}
\] |
[_Riccati] |
✓ |
3.572 |
|
|
\[
{}y^{\prime } = y^{2}+a x \cosh \left (b x \right )^{m} y+a \cosh \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
7.063 |
|
|
\[
{}y^{\prime } = \left (a \cosh \left (\lambda x \right )^{2}-\lambda \right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
15.785 |
|
|
\[
{}2 y^{\prime } = \left (a -\lambda +a \cosh \left (\lambda x \right )\right ) y^{2}+a +\lambda -a \cosh \left (\lambda x \right )
\] |
[_Riccati] |
✓ |
14.837 |
|
|
\[
{}y^{\prime } = y^{2}-\lambda ^{2}+a \cosh \left (\lambda x \right )^{n} \sinh \left (\lambda x \right )^{-n -4}
\] |
[_Riccati] |
✗ |
14.779 |
|
|
\[
{}y^{\prime } = a \sinh \left (\lambda x \right ) y^{2}+b \sinh \left (\lambda x \right ) \cosh \left (\lambda x \right )^{n}
\] |
[_Riccati] |
✓ |
6.556 |
|
|
\[
{}y^{\prime } = a \cosh \left (\lambda x \right ) y^{2}+b \cosh \left (\lambda x \right ) \sinh \left (\lambda x \right )^{n}
\] |
[_Riccati] |
✓ |
7.555 |
|
|
\[
{}\left (a \cosh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \cosh \left (\mu x \right ) y-d^{2}+c d \cosh \left (\mu x \right )
\] |
[_Riccati] |
✗ |
149.561 |
|
|
\[
{}\left (a \cosh \left (\lambda x \right )+b \right ) \left (y^{\prime }-y^{2}\right )+a \,\lambda ^{2} \cosh \left (\lambda x \right ) = 0
\] |
[_Riccati] |
✓ |
4.349 |
|
|
\[
{}y^{\prime } = y^{2}+a \lambda -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✗ |
23.625 |
|
|
\[
{}y^{\prime } = y^{2}+3 a \lambda -\lambda ^{2}-a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✗ |
24.696 |
|
|
\[
{}y^{\prime } = y^{2}+a x \tanh \left (b x \right )^{m} y+a \tanh \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
5.931 |
|
|
\[
{}\left (a \tanh \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \tanh \left (\mu x \right ) y-d^{2}+c d \tanh \left (\mu x \right )
\] |
[_Riccati] |
✗ |
237.106 |
|
|
\[
{}y^{\prime } = y^{2}+a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✗ |
23.498 |
|
|
\[
{}y^{\prime } = y^{2}-\lambda ^{2}+3 a \lambda -a \left (a +\lambda \right ) \coth \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✗ |
25.131 |
|
|
\[
{}y^{\prime } = y^{2}+a x \coth \left (b x \right )^{m} y+a \coth \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
6.107 |
|
|
\[
{}\left (a \coth \left (\lambda x \right )+b \right ) y^{\prime } = y^{2}+c \coth \left (\mu x \right ) y-d^{2}+c d \coth \left (\mu x \right )
\] |
[_Riccati] |
✗ |
216.248 |
|
|
\[
{}y^{\prime } = y^{2}-2 \lambda ^{2} \tanh \left (\lambda x \right )^{2}-2 \lambda ^{2} \coth \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
20.898 |
|
|
\[
{}y^{\prime } = y^{2}+a \lambda +b \lambda -2 a b -a \left (a +\lambda \right ) \tanh \left (\lambda x \right )^{2}-b \left (b +\lambda \right ) \coth \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
22.665 |
|
|
\[
{}y^{\prime } = a \ln \left (x \right )^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{2 m} \ln \left (x \right )^{n}
\] |
[_Riccati] |
✗ |
3.740 |
|
|
\[
{}y^{\prime } x = a y^{2}+b \ln \left (x \right )+c
\] |
[_Riccati] |
✓ |
2.031 |
|
|
\[
{}y^{\prime } x = a y^{2}+b \ln \left (x \right )^{k}+c \ln \left (x \right )^{2 k +2}
\] |
[_Riccati] |
✓ |
36.124 |
|
|
\[
{}y^{\prime } x = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2}+a
\] |
[_Riccati] |
✗ |
1.449 |
|
|
\[
{}y^{\prime } x = x y^{2}-a^{2} x \ln \left (\beta x \right )^{2 k}+a k \ln \left (\beta x \right )^{k -1}
\] |
[_Riccati] |
✗ |
2.369 |
|
|
\[
{}y^{\prime } x = a \,x^{n} y^{2}+b -a \,b^{2} x^{n} \ln \left (x \right )^{2}
\] |
[_Riccati] |
✗ |
2.111 |
|
|
\[
{}x^{2} y^{\prime } = x^{2} y^{2}+a \ln \left (x \right )^{2}+b \ln \left (x \right )+c
\] |
[_Riccati] |
✓ |
7.000 |
|
|
\[
{}x^{2} y^{\prime } = x^{2} y^{2}+a \left (b \ln \left (x \right )+c \right )^{n}+\frac {1}{4}
\] |
[_Riccati] |
✗ |
1.771 |
|
|
\[
{}x^{2} \ln \left (a x \right ) \left (y^{\prime }-y^{2}\right ) = 1
\] |
[_Riccati] |
✓ |
1.435 |
|
|
\[
{}y^{\prime } = y^{2}+a \ln \left (\beta x \right ) y-a b \ln \left (\beta x \right )-b^{2}
\] |
[_Riccati] |
✓ |
2.061 |
|
|
\[
{}y^{\prime } = y^{2}+a x \ln \left (b x \right )^{m} y+a \ln \left (b x \right )^{m}
\] |
[_Riccati] |
✓ |
2.155 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}-a b \,x^{n +1} \ln \left (x \right ) y+b \ln \left (x \right )+b
\] |
[_Riccati] |
✓ |
3.191 |
|
|
\[
{}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{n +1} \ln \left (x \right )^{m} y-a \ln \left (x \right )^{m}
\] |
[_Riccati] |
✓ |
3.462 |
|
|
\[
{}y^{\prime } = a \ln \left (x \right )^{n} y-a b x \ln \left (x \right )^{n +1} y+b \ln \left (x \right )+b
\] |
[_linear] |
✓ |
2.077 |
|
|
\[
{}y^{\prime } = a \ln \left (x \right )^{k} \left (y-b \,x^{n}-c \right )^{2}+b n \,x^{n -1}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
5.122 |
|
|
\[
{}y^{\prime } = a \ln \left (x \right )^{n} y^{2}+b \ln \left (x \right )^{m} y+b c \ln \left (x \right )^{m}-a \,c^{2} \ln \left (x \right )^{n}
\] |
[_Riccati] |
✗ |
3.153 |
|
|
\[
{}y^{\prime } x = \left (a y+b \ln \left (x \right )\right )^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
1.614 |
|
|
\[
{}y^{\prime } x = a \ln \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \ln \left (\lambda x \right )^{m}
\] |
[_Riccati] |
✓ |
74.009 |
|
|
\[
{}y^{\prime } x = a \,x^{n} \left (y+b \ln \left (x \right )\right )^{2}-b
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.601 |
|
|
\[
{}y^{\prime } x = a \,x^{2 n} \ln \left (x \right ) y^{2}+\left (b \,x^{n} \ln \left (x \right )-n \right ) y+c \ln \left (x \right )
\] |
[_Riccati] |
✓ |
5.079 |
|
|
\[
{}x^{2} y^{\prime } = a^{2} x^{2} y^{2}-y x +b^{2} \ln \left (x \right )^{n}
\] |
[_Riccati] |
✓ |
3.027 |
|
|
\[
{}\left (a \ln \left (x \right )+b \right ) y^{\prime } = y^{2}+c \ln \left (x \right )^{n} y-\lambda ^{2}+\lambda c \ln \left (x \right )^{n}
\] |
[_Riccati] |
✗ |
137.631 |
|
|
\[
{}\left (a \ln \left (x \right )+b \right ) y^{\prime } = \ln \left (x \right )^{n} y^{2}+c y-\lambda ^{2} \ln \left (x \right )^{n}+\lambda c
\] |
[_Riccati] |
✗ |
138.026 |
|
|
\[
{}y^{\prime } = \alpha y^{2}+\beta +\gamma \sin \left (\lambda x \right )
\] |
[_Riccati] |
✓ |
2.846 |
|
|
\[
{}y^{\prime } = y^{2}-a^{2}+a \lambda \sin \left (\lambda x \right )+a^{2} \sin \left (\lambda x \right )^{2}
\] |
[_Riccati] |
✓ |
5.925 |
|
|
\[
{}y^{\prime } = y^{2}+\lambda ^{2}+c \sin \left (\lambda x +a \right )^{n} \sin \left (\lambda x +b \right )^{-n -4}
\] |
[_Riccati] |
✗ |
109.819 |
|
|
\[
{}y^{\prime } = y^{2}+a \sin \left (\beta x \right ) y+a b \sin \left (\beta x \right )-b^{2}
\] |
[_Riccati] |
✓ |
3.604 |
|