Problem

(a) Show that the equation dy/dx = f (x,y) is homogeneous if and only if f (tx, ty)...

(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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Solutions For Problems in Chapter 2.6

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