Assignment:
Q1. Solve the boundary-value problem, if possible.
a. y''-6y'+9y =0, y(0) =1 and y(1) = 0
b. 9y''-18y'+10y = 0 , y(0) =0 and y(pie) = 1
Q2. If a, b and c are all positive constants and y(x) is a solution of the differential equation ay''+by'+cy = 0, show that lim x->infinity y(x) = 0
Provide complete and step by step solution for the question and show calculations and use formulas.