Test that the nature differential equation x (dy/dx) - y + xsin (y/x) =0 is-
Answer & explanation
Correct answer: option 1
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.