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.
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
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
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