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

xy = x³/3+ C

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

This ifs of the form dy/dx +Py = Q

where P = 1/x, Q= x

I.F. = e^∫Pdx = e^{∫(1/x) dx} =e^logx = x

The solution of the given differential equation is given by-

y(I.F.) = ∫(Q x I.F.)dx + C

⇒yx = ∫(x.x.)dx + C 

⇒ yx = ∫(x²)dx + C 

⇒xy= x³/3+ C