A differential equation of the form

is called a Bernoulli differential equation. Note that this differential equation is linear for and , and nonlinear otherwise.

(a) Assuming that is not equal to or , show that satisfies the linear differential equation

(b) Use part (a) to solve the IVP

[Hint: You might find the identity useful.]

You should write your solution on paper.  In an exam scenario you would have time after the exam is finished to scan/photograph and upload your solution.