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Show that the DE is exact, then solve it. 2.a²y' + 4.xy = 3 sin x, y(27) = 0

Show that the DE is exact, then solve it. 2.a²y' + 4.xy = 3 sin x, y(27) = 0

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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Question
Show that the DE is exact, then solve it. 2.x2y' + 4.xy = 3 sin a, y(27) = 0
Transcribed Image Text:Show that the DE is exact, then solve it. 2.x2y' + 4.xy = 3 sin a, y(27) = 0
Expert Solution
Step 1

Let us consider first order differential equation dydx+P(x)y=Q(x)

The differential equation is solved by using integrating factor method.

The integrating factor is obtained as  

I.F.=e∫P(x) dx

Then the solution of differential equation  is 

ye∫P(x)dx=∫Q(x)e∫P(x) dx +C

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