POSSIBLE POINTS: 23.76 3. Consider the differential equation dy xy + = 1, where x

3. dy xy Consider the differential equation + dy 4x2 POSSIBLE POINTS: 23.76 = 1, where I X I < 2 andy= 1 whenx= 0. (a) (b) (c) Use Euler's method with h = 0.25, to find an approximate value of y when x = 1, giving your answer to two decimal places. (i) (ii) By first finding an integrating factor, solve this differential equation. Give your answer in the form y =f(x). Calculate, correct to two decimal places, the value of y when x = 1. (10) (10) Sketch the graph of y for 0 s x 1. Use your sketch to explain why your approximate value of y is greater than the true value of y. (4)