Differential Equations and Linear Algebra (4th Edition)

Published by Pearson
ISBN 10: 0-32196-467-5
ISBN 13: 978-0-32196-467-0

Chapter 1 - First-Order Differential Equations - 1.8 Change of Variables - Problems - Page 79: 2

Answer

$f(x,y)$ is not homogeneous of degree zero.

Work Step by Step

Given $$f(x, y)=2x-5y$$ Let \begin{aligned} f (t x, ty)&=2tx-5ty\\ &=t(2x-5y)\\ &\neq f(x,t) \end{aligned} Thus, $f(x,y)$ is not homogeneous of degree zero.
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