Test that the nature differential equation x (dy/dx) - y + xsin (y/x) =0 is-

Homogeneous Non- homogeneous May or may not be homogeneous None of these

Homogeneous

The given differential equation is x (dy/dx) - y + xsin (y/x) =0 ⇒ dy/dx = {y - xsin (y/x)}/x Let F(x,y) = {y - xsin (y/x)}/x ⇒ F(tx,ty) = {ty - txsin (ty/tx)}/tx ⇒ F(tx,ty) = t0. F(x,y)  So, given differential equation is homogeneous differential equation.