ODE
\[ y'(x)=y(x) \left (a+b y(x)^2\right ) \] ODE Classification
[_quadrature]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.245403 (sec), leaf count = 77
\[\left \{\left \{y(x)\to -\frac {i \sqrt {a} e^{a (x+c_1)}}{\sqrt {-1+b e^{2 a (x+c_1)}}}\right \},\left \{y(x)\to \frac {i \sqrt {a} e^{a (x+c_1)}}{\sqrt {-1+b e^{2 a (x+c_1)}}}\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 70
\[\left [y \left (x \right ) = \frac {\sqrt {\left (\textit {\_C1} a \,{\mathrm e}^{-2 a x}-b \right ) a}}{\textit {\_C1} a \,{\mathrm e}^{-2 a x}-b}, y \left (x \right ) = -\frac {\sqrt {\left (\textit {\_C1} a \,{\mathrm e}^{-2 a x}-b \right ) a}}{\textit {\_C1} a \,{\mathrm e}^{-2 a x}-b}\right ]\] Mathematica raw input
DSolve[y'[x] == y[x]*(a + b*y[x]^2),y[x],x]
Mathematica raw output
{{y[x] -> ((-I)*Sqrt[a]*E^(a*(x + C[1])))/Sqrt[-1 + b*E^(2*a*(x + C[1]))]}, {y[x] -> (I*Sqrt[a]*E^(a*(x + C[1])))/Sqrt[-1 + b*E^(2*a*(x + C[1]))]}}
Maple raw input
dsolve(diff(y(x),x) = y(x)*(a+b*y(x)^2), y(x))
Maple raw output
[y(x) = 1/(_C1*a*exp(-2*a*x)-b)*((_C1*a*exp(-2*a*x)-b)*a)^(1/2), y(x) = -1/(_C1*a*exp(-2*a*x)-b)*((_C1*a*exp(-2*a*x)-b)*a)^(1/2)]