Cauchy Method/ UC set OR Variation of Param?

[dgutierrez079]

Hello new to this forum , Was solving some Diff eq problems and iam getting two different answers using two methods, ok the problem is i=primes (x^2)(y^ii)+(x)(y^i)+y=4sin(lnx)
This is cauchy method, When i use variation of parameters i get a long answer with impossible integrals and when i use Undetermined coefficients i also get an answer, Not sure witch is correct i also understand that Uc method can't be used with tanx, secx, lnx, but in this case that there is a sin in there iam not sure. Thanks

 

[HallsofIvy]

Please show what you did and what answer you got.

(Note that the substution u= ln(x) turns this into the differential equation with constant coefficients, y''+ y= ln(u) where the primes now indicate differentiation with respect to u.)