Calculus

(ii) Solve the following initial value problem dy - Inz; y (1) = 2 (5) (iii) A bactrial culture contains 100 cells at a certain point in time. Sixty minutes later, there are 450 cells. Assuming exponential growth, determine the number of cells present at time t. (5) I (b) If f (z, y) = 12 + y Determine (i) f= and fu (1) Use your answers in b(i) above to write down dy (iii) Confirm your answer in b(ii) by finding dy using implicit differentiation. [25]QUESTION 4 (a) Use the method of separation of variables to (i) Solve the differential equation dy cos (I) (1 + y?) y sin (I)