Use separation of variables to solve the initial value problem.

Question

(dy)/(dx)=2xcos^(2)y; y(3)=0

Answer 1

dy/cos²y = 2xdx; ∫sec²ydy = ∫2xdx; tany = x² + C; tan0 = 3² + C; C = - 9.

So, tany = x² - 9