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Question

For the differential equation sin2xdydxy=tanx; and y(π4)=2 Find the value of the constant.

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Solution

Given, sin2xdydxy=tanx
dydxycsc2x=sinxcosx.12sinxcosx
dydxycsc2x=sec2x2 ...(1)
Here P=csc2xPdx=csc2xdx=12log(tanx)=log(tanx)12
I.F.=elog(tanx)12=(tanx)12
Multiplying (1) by I.F. we get
(tanx)12dydxy(tanx)12csc2x=(tanx)12sec2x2
Integrating both sides, we get
y=tanx+ctanx
As y(π4)=2
2=1+c
c=1

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