consider the DE: y''+x2y'+x2y=0 about the ordinary point x=0 a) find the recurrence relation, and indicate...
consider the DE: y''+x2y'+x2y=0 about the ordinary point x=0
a) find the recurrence relation, and indicate if any of the coefficients are equal to zero .(if any)
b) use the recurrence relation to write the first four nonzero terms of each of the two linearly independent power series near the ordinary point x=0.
My attempt...
after plugging in the y, y' , and y'' power series. I got something that looked like
2a2+6a3x + sigma from n=2 -> to infinity of [an+2 (n+2)(n+1) + an-1 (n-1) + an-2] xn=0
but I feel it should be a three-term recurrence relation and not two like up there. can u help me? what did I do wrong? I can't seem to find any example online or anywhere on what to do when the y in the question has an x or x2.
Homework Answers
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