The nonlinear equation dy/dt +p(t) y = q(t) ya (where a ≠ 0, a ≠ 1) is called a Bernoulli equation and can be transformed into a linear equation. It already looks almost linear, except for ya on the right side.
(a) Divide (19) by y" and then show that the transformation v = y1-a reduces (19) to a linear equation in v.
(b) Use the transformation in (a) to solve the Bernoulli equation y' - y = y3.
(c) Explain how to solve the given Bernoulli equation when a = 0 and when a = 1.