dv = − ∫

dv = − ∫ dx log( = − 2log − = c x = c Now, Replace v = y    = c xy = c is the solution. Example . Find the particular solution of the differential equation x dy y x y dx given that x x dy y x y dx = x dy = − y x y dx = − xy ( ) Put y vx and dy x dv in  ( ) x dv xvx v x = − v x dv = − = − On separating the variables dv = − dx dv v v + = − dx v v dv