Answer
Exact
Work Step by Step
$2xe^y dx+(3y^2+x^2e^y) dy=0$ _____(1)
Here
$$M(x,y)=2xe^y$$
$$N(x,y)=3y^2+x^2e^y$$
$$M_{y}=2xe^y$$
$$N_{x}=2xe^y$$
\[M_{y}=N_{x}\]
Therefore (1) is exact differential equation
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 - Problems - Page 92: 4
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