general solution of high DE using reduction of order

Question

find the general solution of the DE ..... y1 = x^1/2

4x²y''+y=24x^1/2ln(x)

I reduced the DE to first linear by letting w = u'

w' +1/x w = 6ln(x) / x²

found u to be ln³(x)+ln(x)c1+c2

my general solution is:

y= x^1/2ln³(x)+x^1/2ln(x)c1+x^1/2c2

which means that the particular solution yp is x^1/2ln³(x)

please let my know if my answer is correct.

Thank you.

Answer 1

Yes, it's correct. BTW, you can go to wolframalpha.com and input "solve for y in 4*x^2*y''+y=24*x^(.5)*log(x)" and get the complete answer for comparison.