How to Find Degree of Homogeneous Function

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$SOLVED:Determine if each function is homogeneous. If it is, find its degree. f(x, y)=x^{3}-x y y^{3}$

SOLVED:Determine if each function is homogeneous. If it is, find its degree. f(x, y)=x^{3}-x y y^{3}

2021年3月28日

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A function f is called homogeneous of degree n if it satisfies the equation f(t x, t y)=t^n f(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)=x^2 y 2 x y^2 5 y^3 is homogeneous of degree 3 . (b) Show that if f is homogeneous of degree n, then x (∂f)/(∂x) y (∂f)/(∂y)=n f(x, y) [Hint: Use the Chain Rule to differentiate f(t x, t y) with respect to t .1] | Numerade

2020年8月6日

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SOLVED: From the given, find the degree of homogeneous ODE f(x,y) = 4x^4 - 7xy^3 y^4

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SOLVED:Determine whether the given function is homogeneous of degree zero. Rewrite those that are as functions of the single variable V=y / x. f(x, y)=(√(x^2 y^2))/(x), x<0

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Given F(u)=V(x, y, z) where V is a homogeneous function of x, y, z of degree n, prove that x (∂u)/(∂x) y (∂u)/(∂y) z (∂u)/(∂z)=n (F(u))/(F^'(u)) | Numerade

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VIDEO solution:A function f is called homogeneous of degree n if it satisfies the equation f(t x, t y)=t^n f(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)=x^2 y 2 x y^2 5 y^3 is homogeneous of degree 3 . (b) Show that if f is homogeneous of degree n, then x (∂f)/(∂x) y (∂f)/(∂y)=n f(x, y) [Hint: Use the Chain Rule to differentiate f(t x, t y) with respect to t. ] | Numerade

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SOLVED:Determine in each exercise whether or not the function is homogeneous. If it is homogeneous, state the degree of the function. 4 x^2-3 x y y^2

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Show that the differential equation 2y^(x/y) dx (y − 2x e^(x/y)) dy = 0 is homogeneous. Find the particular solution of this differential equation, given that x = 0 when y = 1. - Mathematics | Shaalaa.com

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