4.2.31 $y^{\prime }(x)=y(x)(a+by(x{)}^2)$

ODE
$$y^{\prime }(x)=y(x)(a+by(x{)}^2)$$ ODE Classification

[_quadrature]

Book solution method
The Bernoulli ODE

Mathematica ✓
cpu = 0.0339076 (sec), leaf count = 77

$$\{\{y(x)\to -\frac{i\sqrt{a}{e}^{a(c_1+x)}}{\sqrt{b{e}^{2a(c_1+x)}-1}}\},\{y(x)\to \frac{i\sqrt{a}{e}^{a(c_1+x)}}{\sqrt{b{e}^{2a(c_1+x)}-1}}\}\}$$

Maple ✓
cpu = 0.005 (sec), leaf count = 21

$$\{\frac{b}{a}-{\mathrm{e}}^{-2ax}\mathit{\_}\mathit{C}\mathit{1}+{\left(y\left(x\right)\right)}^{-2}=0\}$$ 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),'implicit')

Maple raw output

1/a*b-exp(-2*a*x)*_C1+1/y(x)^2 = 0