Differential equations

[Anon No.15296910]

y'=3y/x+1+x, the differential equation
already I summarize :
1.the particular solution is kx^3, k real
2.I can't find the right solution with the method of the variation of the constant
I calculated ;
y=g(x)x^3 y'=g(x)'x^3+3g(x)x^2
I replace in my equation and I get
g' =(1+x)/x^3, except that this calculation is wrong according to the computer and the official correction
I don't see the error in my reasoning at all

[Anonymous No.15296973]

g' = (1+x)/x^3
g= -1/(2x^2) - 1/x + C
y = -x/2 - x^2 + C x^3

Yes this solves the equation

[Anon No.15296984]

yes sorry