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

⇒yx = (xsinx + cosx) + C

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

This ifs of the form dy/dx +Py = Q

where P = 1/x, Q= cos x

I.F. = e^∫Pdx = e^∫(1/x)dx =x 

The solution of the given differential equation is given by-

y(I.F.) = ∫(Q xI.F.)dx + C

⇒yx = ∫(cosx.x)dx + C 

⇒yx =(xsinx+cosx) + C