Question

Solve this second order series example:. y''-xy'+2y=0. It must be solved by power series, with a center a, finding the recurrent formula, and two linearly independent solutions.

Answer 1

For the problem presented, this is what it would look like if you combine the terms of the series 2c0x0+2c2x0+∑n=1∞[an+2(n+1)(n+2)−ann−2an]=0

And then…

2c0 + 2c2 = 0 and c2 = −c0

So it would go something like this.

 

Y = (1 − x2) c0

I am hoping that this answer has satisfied your query about this specific question.