Solve Second Order ODE: Find a Values for Zero Tendency

[tracedinair]

Homework Statement

Find all values of a for which all solutions of

y''(x) + (a/x)y'(x) + (5/2)y(x) = 0

tend to zero as x tends 0⁺ and all values for which all solutions tend to zero as x tends to +

Homework Equations

The Attempt at a Solution

I am not even sure where to being with this problem. My guess is to examine all cases for b-(a²/4). Just not really sure on this at all.

 

[Bacat]

You should know the http://math.colgate.edu/~wweckesser/math311/handouts/second_order.pdf" to a second-order differential equation to solve this.

Then look at the possible solutions based on what you have for a and x.