Can someone help me i don't understand this DE

[iScience]

problem: xy''-4y'=x^4

when i solve it i get y(homogeneous)=C1+C2x^5 which is fine because that's what the back of the book says

but for the particular solution, i get .. C1=-(1/25)x^5 , C2=(1/5)lnx

so y(general)= C1+C2x^5-(1/25)x^5+(1/5)lnx(x^5)

but wolframalpha as well as the back of my book both say the answer is...
y(general)=C1+C2x^5+(1/5)lnx(x^5)

where does the -(1/25)x^5 term go?...

 

[Integral]

You have
C₁ x⁵ + C₂ x⁵ = C₃x⁵

Does that help?

 

[iScience]

so technically my answer is correct and they just combined the x^5 terms.. i see

 

[iScience]

Thanks!

 

[Ackbach]

If you're finding the general solution of an ODE, then usually you would not allow pieces of the homogeneous solution to show up in the particular solution.