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For the differential equation y'' + 42y' + 152y = = 8 cos(8x)

For the differential equation y'' + 42y' + 152y = = 8 cos(8x)

Advanced Engineering Mathematics
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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For the differential equation Answer to the previous part: Y'p (x) = − 8A sin(8x) + 8B cos(8x) Next, find the second derivative of your guess. Use A and B for arbitrary constants. Y''p (x) р y'' +42y' + 152y = 8 cos(8x) =
Transcribed Image Text:For the differential equation Answer to the previous part: Y'p (x) = − 8A sin(8x) + 8B cos(8x) Next, find the second derivative of your guess. Use A and B for arbitrary constants. Y''p (x) р y'' +42y' + 152y = 8 cos(8x) =
Expert Solution
Step 1: Given Information:

Given that the differential equation is:

                              y apostrophe apostrophe plus 42 y apostrophe plus 152 y equals 8 cos left parenthesis 8 x right parenthesis comma

and Y apostrophe subscript P left parenthesis x right parenthesis equals negative 8 A sin left parenthesis 8 x right parenthesis plus 8 B cos left parenthesis 8 x right parenthesis.

Where A space a n d space space B spaceare arbitrary constant.

To find the second derivative of Y subscript P left parenthesis x right parenthesis.

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