In each part, use separation of variables to solve the given differential equation (find all solutions). (i) y′=(y−3)² cost (ii) dt/dy = 2y(1+t2 )*1.b) In each part, use your answers to part a) to solve the initial value problem. That is, find the solution of the given differential equation satisfying the given initial condition. (i) y
=(y−3)² cost,y(0)=0. (ii) y′=(y−3)² cost,y(0)=3. (iii) dt/dy= 2y(1+t2)/1 ,y(0)=2. (iv) dt/dy = 2y(1+t 2)/1 ,y(0)=−3.