(a) Solve the following initial value problem (b) Given that cos y 3 = 0, (1) = 3 G(x,y)=7y+cos (xy) -zy. (i) Find the first partial derivatives G. and Gy. dy (ii) Write down. using your answer to b(i) above. dr (iii) If G (r, y) = 0, confirm your answer in b(ii) above by using implicit differentiation. dz (c) Use the chain rule for partial derivatives to find r=u+ and y= uv. when u 0 and v= 1, if == sin(ay)+sin y. (5) (d) A bacterial culture starts with 1000 bacteria and after 2 hours there are 2500 bacteria. Assuming that the culture grows at a rate proportional to its size, find the population after 4 hours. (5) [25] Total: [100]