QaFind a selution.{ determine an explicit galution):haly (0)b) Graph the solu tionc) What is the limit yx) as xy∞? Invchi odt boitti pailpn8.

Answered: QQFind a solvtion y(x) ( determine an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

QaFind a selution.
{ determine an explicit galution):hal
y (0)
b) Graph the solu tion
c) What is the limit yx) as xy∞? Invchi odt boit
ti pailpn
8.

Expert Solution

Step 1

part (a)

Given differential equation

$y^{'} e^{2 x + y} = \cos 3 x$

Explanation

$\begin{array}{l} y^{'} e^{2 x + y} = \cos 3 x \\ \Rightarrow y^{'} e^{2 x} e^{y} = \cos 3 x \\ \Rightarrow d y e^{y} = e^{- 2 x} \cos 3 x d x \end{array}$

Integrating both the sides

$\int e^{y} d y = \int e^{- 2 x} \cos 3 x d x ... (i)$

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