b). A nonlinear differential equation of the form $y' + p(x)y = q(x)y^n$ is called a Bernoulli equation.
i). Solve Bernoulli's equation when $n = 0$.
ii). Show that if $n \neq 0, 1$, then the substitution $z = y^{1-n}$ reduces Bernoulli's equation to a linear equation.
iii). Hence, solve the differential equation $y' = xy + xy^2$.
