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Question

If the solution of the differential equation dydxy=1=ex and y(0)=y0 has a finite value, where x, then
the value of |2y0| is

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Solution

dydxy=1ex
yex=ex+12e2x+c
y=1+12ex+cex
x=0,y=y0
so, c=y0+12
y=1+12ex+(y0+12)ex
x,y finite value so y0+12=0
y0=12
|2y0|=4

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