Advanced Maths Differential Equation

4 [Maximum mark: 19] Nov 2013 Consider the differential equation ay y for x, y > 0. dx x+ xy (a) Use Euler's method starting at the point (x, y) = (1,2), with interval h =0.2, to find an approximate value of y when x = 1.6. [7] dv V (b) Use the substitution y = vx to show that x- dx 1+ vv - V; [3] 22 (c) (i) Hence find the solution of the differential equation in the form f(x, y) =0, given that y =2 when x =1. (ii) Find the value of y when x = 1.6. [9]