Thread: differential equation

Using the fact that y1 = x^(−1/2)cosx is a solution of the associated homogeneous problem, obtain the general solution of the ODE
(x^2)y′′ + (x)y′ + (x^2−1/4)y = x^(3/2)

do i divide everything by x^2 and do wronskian?
do i use y = x^m, y'=mx^(m-1), and y''=m(m-1)x^(m-2)?

or do i find y2?

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-he...order-ode.html

Kind regards