differential equations - No result from DSolve (evaluation keeps running)

No answer is given and no error message as well for this expression.

DSolve[X*Y''[X] + (3*X^3 - 1) Y'[X] == C, Y[X], X]

Hope someone can help me. I really appreciate that.

Answer

Try:

sol = First@Block[{Integrate}, DSolve[X*Y''[X] + (3*X^3 - 1) Y'[X] == C, 
Y[X], X] /. {Integrate -> Inactive[Integrate]}] // Simplify

$\left\{Y(X)\to \int _1^X\exp \left(\int _1^{K[3]}\left(\frac{1}{K[1]}-3 K[1]^2\right)dK[1]\right) \left(c_1+\int _1^{K[3]}\frac{C \exp \left(-\int _1^{K[2]}\left(\frac{1}{K[1]}-3 K[1]^2\right)dK[1]\right)}{K[2]}dK[2]\right)dK[3]+c_2\right\}$

Activate[sol] (* Integrate can't find closed solution *)

Solution by Maple 2017.3: