Solution Found!
(a) Show that the equation dy/dx = f (x,y) is homogeneous
Chapter 2, Problem 43E(choose chapter or problem)
(a) Show that the equation dy/dx = f (x,y) is homogeneous if and only if f (tx, ty) = f (x,y). [hint: let t = 1/x.](b) A function H(x,y) is called homogeneous of order n if H(tx,ty) = tn H (x,y). Show that the equation is homogeneous if M (x,y) and N (x,y) are both homogeneous of the same order
Questions & Answers
QUESTION:
(a) Show that the equation dy/dx = f (x,y) is homogeneous if and only if f (tx, ty) = f (x,y). [hint: let t = 1/x.](b) A function H(x,y) is called homogeneous of order n if H(tx,ty) = tn H (x,y). Show that the equation is homogeneous if M (x,y) and N (x,y) are both homogeneous of the same order
ANSWER:Solution:Step 1:In this problem, we have to show these conditions are homogeneous, which is the form of dy/dx = f(x,y).