The solution of the differential equation y' = (x+y)/x is-

 The given  differential equation is y' = (x+y)/x

which can be written as dy/dx = (x+ y)/ x.....................(i)

This is an homogeneous differential equation.

Let y = vx

⇒dv/dx = v + x (dv/dx)

substituting the values of v and dv/dx in equation (i) we get:

v+ x (dv/dx) = {x +(vx)}/x

⇒ v + x(dv/dx) = (1+v)

⇒dv = dx/x

on integrating both sides, we get:

v = xlogx + C

since v= y/x

⇒ y/x = xlogx +c

⇒ y = x log x + Cx