# differential equation

• April 26th 2009, 05:25 PM
ynotidas
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?
• April 27th 2009, 07:33 AM
chisigma
The procedure to arrive, once you know a solution $y_{1}$ of this type of equation, to a second solution $y_{2}$ independent from it, is illustrated here...

http://www.mathhelpforum.com/math-he...order-ode.html

Kind regards

$\chi$ $\sigma$