plutions of differential equation ху" 1+ y2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Find all solutions of differential equation
xy" =
1+ y2
Transcribed Image Text:Find all solutions of differential equation xy" = 1+ y2
Expert Solution
Step 1

Consider given differential equation put y” =t’ and y’ =t

xt'=1+t2

dt1+t2=dxx

sinh-1t=logxc

t =sinh(logxc)

dydx=elogxc-e-logxc2

dydx=xc2-12xc

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