The procedure to arrive, once you know a solution of this type of equation, to a second solution independent from it, is illustrated here...
http://www.mathhelpforum.com/math-help/calculus/82519-variation-parameter-2nd-order-ode.html
Kind regards
Given that y=x is a solution of:
(X^2)y"-(2x+5x^2)y'+(2+5x)y=0 in x>0,
Find another solution yc of the same equation such that {x,yc} is a fundamental set of solutions.
yc = ?
What do I do? I wanted to use series solutions, but it's a singular point. So then I decided to try using reduction of order to get y2 = uy1 (where you solve for u' and integrate, etc). However, that turned into an unsolvable integral... so I'm stuck! Please help!
The procedure to arrive, once you know a solution of this type of equation, to a second solution independent from it, is illustrated here...
http://www.mathhelpforum.com/math-help/calculus/82519-variation-parameter-2nd-order-ode.html
Kind regards