Homework 5 Due Wednesday 9/30/9 - This is crucial practice for the mid-term.

 

A) Section 3.2 [Total 16 marks, 4 marks each]

Problems 1. and 3. 'Find Wronskian'


Check that y_1 and y_2 are solutions of the given ODE. Do they constitute a fundamental set of solutions?

1) y" +4y = 0, y_1 (t) = cos 2t   and   y_2 (t)  = sin 2t

2) y" -2y'+y =0,  y_1 (t) = exp(t)  and  y_2 (t) = t exp(t)

(This is 23 and 24 in the 8th ed. and 24. and 25. in the 9th ed.)



B) What is the general form of the Wronskian for the differential equation

1) y" + cost y' + ty = 0?

2) ty" + 6ty' +cost y = 0?

[Total 10, 5 Marks each]

 

C) Find the general solution of

1) y" -2y'+2y =0

2) y" +6y"+13y = 0

[Total 12 marks, 6 marks each]

HINT: We'll learn how to do C) on friday

+2 marks for presentation