School of Mathematical Sciences Engineering Mathematics IIA, MATHS 2201 Assignment 8 question sheet Due: Tuesday, 16/05/2017 (Week 10), by 12.00pm When presenting your solutions to the assignment, please include some explanation in words to accompany your calculations. It is not necessary to write a lengthy description, just a few sentences to link the steps in your calculation. Messy, illegible or inadequately explained solutions may be penalised. The marks awarded for each part are indicated in brackets. CHECKLIST \u0003: Have you completed and attached a coversheet? \u0003: If before the deadline, have you submitted your assignment into the correct hand-in box (EMG05)? \u0003: If after the deadline, but within 24 hours, have you contacted us via the enquiry page on MyUni and then submitted your assignment into the late hand-in box (Level 6, Ingkarni Wardli)? \u0003: If more than 24 hours late, do not hand-in your assignment, it will not be marked. 1. Consider the following ordinary differential equation on the interval x > 0, y + 6y + 9y = x2 e3x . (1) (a) State the associated homogeneous equation for (1). (b) Find two linearly independent solutions to the associated homogeneous equation. (c) Using the Wronskian test, show that your two solutions are linearly independent. (d) Using the method of variation of parameters, find the particular integral yp , for the nonhomogeneous equation (1). (e) Thus state the general solution for the nonhomogeneous equation (1). [14 marks] 2. Solve the following initial value problems using eigenvalues \u0014 \u0015 \u0012 \u0013 1 1 2 (a) y = y, y(0) = . 0 2 4 \u0014 \u0015 \u0012 \u0013 1 1 1 (b) y = y, y(0) = . 1 1 0 [26 marks] 3. Find the general solution of x2 y + xy + y = 1, x > 0. [17 marks]