Find the general solution of the differential equation. xy + y' = 138x

use an integrating factor

y' + xy = 138x

I F = e ∫ xdx = e ^ (x^2/2)

y' e^ (x^2/2) + xy e^x^2/2 = 138x e^x^2/2

x y * e^x2/2 = 138∫x e^x^2/2 dx

xy * e ^ (x^2/2) = 138 e^ (x^2/2)

y = 138 / x + c