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If y dy 1 dx = x satisfies the IVP y(1) = 0, then lim y(x) =

If y dy 1 dx = x satisfies the IVP y(1) = 0, then lim y(x) =

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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If y dy 1 = dx x' then lim y(x) = satisfies the IVP y(1) = 0,
Transcribed Image Text:If y dy 1 = dx x' then lim y(x) = satisfies the IVP y(1) = 0,
Expert Solution
Step 1

Given  the IVF as dydx=1x       y(1)=0 

first, solve the problem to find y(x)

so,

dy=dxxnow integrating both side ∫dy=∫dxxy=ln(x)+C

now put x=1and y=0

0=ln(1)+C

C=0

so,

y=ln(x)

 

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