Question: A function f is called homogeneous of degree n if it satisfies the equation f (tx, ty) = t n f (x, y) for all

A function f is called homogeneous of degree n if it satisfies the equation f (tx, ty) = tⁿf (x, y)
for all t, where n is a positive integer and f has continuous second-order partial derivatives.
(a) Verify that f (x, y) = x²y + 2xy² + 5y³ is homogeneous of degree 3.
(b) Show that if f is homogeneous of degree n, then af -nf(x, y) af + y* ду дх

af -nf(x, y) af + y*

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