Show that if is homogeneous of degree then [Hint: Let Find and then let t 1.]
Chapter 13, Problem 65(choose chapter or problem)
Show that if f(x, y) is homogeneous of degree n then
\(x f_{x}(x, y)+y f_{y}(x, y)=n f(x, y)\)
[Hint: Let \(g(t)=f(t x, t y)=t^{n} f(x, y)\). Find \(g^{\prime}(t)\) and then let t = 1.]
Text Transcription:
xf_x(x,y)+yf_y(x,y)=nf(x,y)
g(t)=f(tx,ty)=t^nf(x,y)
g^prime(t)
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