The equation I am entering is 𝑥2𝑦′′ +𝑥𝑦′ +𝑦=4ln(𝑥) and it looks like

DSolve[x^2 y''[x] + xy'[x] + y[x] == Exp[4 Log (x)], y[x], x]

, it comes out as

{{y[x] -> Sqrt[x] C[1] Cos[1/2 Sqrt[3] Log[x]] + 
Sqrt[x] C[2] Sin[1/2 Sqrt[3] Log[x]] + 
Sqrt[x] Cos[
  1/2 Sqrt[3] Log[x]] Inactive[Integrate][-((
   2 Sin[1/2 Sqrt[3] Log[K[1]]] (E^(4 Log K[1]) - 
      Derivative[1][xy][K[1]]))/(Sqrt[3] K[1]^(3/2))), {K[1], 1, 
   x}] + Sqrt[x]
  Sin[1/2 Sqrt[3] Log[x]] Inactive[Integrate][(
  2 Cos[1/2 Sqrt[3] Log[K[2]]] (E^(4 Log K[2]) - 
  Sqrt[3] K[2]^(3/2)), {K[2], 1, x}]}}

I apologize for how it looks, but I do not how what I am doing wrong. I feel like I have tried everything to fix it, but nothing works. If someone could tell me what to do it would be greatly appreciated.

  • 1
    $\begingroup$ You probably need a space between x and y' in the term xy'[x] $\endgroup$
    – mattiav27
    Nov 14 '21 at 19:42
  • $\begingroup$ Also change parentheses after Log to [ ] : DSolve[x^2 y''[x] + x y'[x] + y[x] == Exp[4 Log [x]], y[x], x] $\endgroup$
    – Syed
    Nov 14 '21 at 19:45
  • $\begingroup$ Thank you! Those both seemed to help. I'll definitely try to keep those two things in mind in the futre. $\endgroup$
    – ZachWyman
    Nov 14 '21 at 19:50