promitheus
New member
 Joined
 Aug 19, 2017
 Messages
 18
Hello, having a bit of trouble with how to proceed with this power series problem.
Here is the question:
Consider a power series solution to differential equation y′′+(1 +x^2)y′+(1−x^2)y= 0.
(a) Derive a recurrence relation for the coefficients an.
(b) Now suppose a0= 1 and a1= 0. Use your answer to (a) to evaluate a2, a3, a4, and a5
I'm having trouble with getting a useful recurrence relation. I suspect I have made some rookie mistake in my attempt to match the power x for all terms. Any guidance would be much appreciated. I have attached my working.
Here is the question:
Consider a power series solution to differential equation y′′+(1 +x^2)y′+(1−x^2)y= 0.
(a) Derive a recurrence relation for the coefficients an.
(b) Now suppose a0= 1 and a1= 0. Use your answer to (a) to evaluate a2, a3, a4, and a5
I'm having trouble with getting a useful recurrence relation. I suspect I have made some rookie mistake in my attempt to match the power x for all terms. Any guidance would be much appreciated. I have attached my working.
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