
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^(m1), and y''=m(m1)x^(m2)?
or do i find y2?

The procedure to arrive, once you know a solution $\displaystyle y_{1}$ of this type of equation, to a second solution $\displaystyle y_{2}$ independent from it, is illustrated here...
http://www.mathhelpforum.com/mathhe...orderode.html
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$