(a) Show that the equation dy/dx = f (x,y) is homogeneous

Chapter 2, Problem 43E

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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

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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).

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