Answer
False
Work Step by Step
Differential equation
$\;M(x,y)dx+N(x,y)dy=0$
is exact for for all $x$ ,$y$ in region $R$ if and only if
$M_y=N_x$
And the condition given in question is $M_x=N_y$ that's why given statement is false.
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 - 1.9 Exact Differential Equations - True-False Review - Page 91: a
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