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 - 1.3 The Geometry of First-Order Differential Equations - Problems - Page 32: 13

Answer

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Work Step by Step

We are given: $y'=x\sin(x+y)$ $\frac{\partial f}{\partial y}=x \cos (x+y)$ These equations are continuous along the entirety of the (x,y) plane, thus: $y'=x \sin (x+y)$ $\rightarrow y(0)=1$ By the Existence and Uniqueness Theorem, the differential has a unique solution.
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