Consider the differential equation x2 dy = y' -2x' for x > 0 and y > 2x. It is given that y = 3 when x = 1. dx (a) Use Euler's method, with a step length of 0.1 , to find an approximate value of y when x = 1.5. (b) Use the substitution y = vx to show that x- = v - v-2. dv dx 8x+ x (c) (i) By solving the differential equation, show that y = 4-x (ii) Find the actual value of y when x = 1.5. 8x+ x (iii) Using the graph of y = 4-x3 , suggest a reason why the approximation given by Euler's method in part (a) is not a good estimate to the actual value of y at x = 1.5