solve the given initial value problem, ydx+x(inx-iny-1)dy=0, y(1)=e

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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solve the given initial value problem, ydx+x(inx-iny-1)dy=0, y(1)=e

Expert Solution
Step 1

The given differential equation is,

ydx +xlnx - lny-1dy=0          ................1

The given condition is y1=e                  ................2

 

Now solving the given equation,

ydx +xlnx - lny-1dy=0 ydx + xlnxy-1dy=0                                  ln(a)-ln(b)=lnabxlnxu-1dy=-ydxdydx=-yxlnxy-1                             .................3

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