Find the general solution dy + cos(x)y = cos(x) dx O y = 1+ ke-2 sin(x) O y² = 2 sin(x) + c y = e-sin(x) + cos(x) esin(x) + c O ○ y = sin(x) + ke¯sin(x)
Find the general solution dy + cos(x)y = cos(x) dx O y = 1+ ke-2 sin(x) O y² = 2 sin(x) + c y = e-sin(x) + cos(x) esin(x) + c O ○ y = sin(x) + ke¯sin(x)
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
Transcribed Image Text:Find the general solution
dy + cos(x) y = cos(x)
dx
○ y = 1+ ke-2 sin(x)
Oy²
y²
= 2 sin(x) + c
y=e=sin(x) +
cos(x)
esin(x)
+ c
Oy=sin(x) + ke¯ sin(x)
Expert Solution
Step 1
Given differential equation is .
We have to find the general solution of the given differential equation.
The differential equation is in the standard form of
Here, .
Now, first find the integrating factor, which is given by
Hence, .
Step by step
Solved in 2 steps
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