Question

2a,2b, and 2c

1. Assuming x > 0, find the general solution of the following Euler equa- tions. f) 5x2y" +12xy' +2y = 0 g) 2y"xy 0 h) a2y" - 2xy =0 i) a2y"-ay-n(n + 2)y 0, where n is a positive integer a) x2y"-3ay 4y 0 b) x2y"-5ay +10y 0 c) 6x2y" +7xy - y 0 d) xy"y0 e) x2y"-3ay' +13y 0 2. Find the solution of the following problems. Before doing these prob- lems, you might want to review Exercise 3, on page 63. a) x2y"- 2ay 2y xe, where y(1) 0, and y(1) 0 b) x2y"- 4xy/4y = -2a2 +1, where y(1) 0, and y'(1) = 0 c) a2y"- xy y = In a, where y(1) 0, and y'(1) 0 d) xy"+yx, where y(1) 1, and y'(1) =-1 e) (x- 1)2y"+(x - 1)y -y 0, where y(2) = 1, and y'(2) 0

Answer 1

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