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Question

The integrating factor of xcosx(dydx)+(xsinx+cosx)y=1 is

A
xcosx
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B
xsinx
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C
xsecx
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D
xcscx
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Solution

The correct option is B xsecx
xcosxdydx+(xsinx+cosx)y=1
dydx+(xsinx+cosx)yxcosx=1xcosx
It is first degree linear D.E on comparing with
dydx+Py=Q ,we get
P=(xsinx+cosx)xcosx
=tanx+1x
I.F=ePdx
=e(tanx+1x)dx
=e(log(secx)+log(x))
=elog(xsecx)
=xsecx

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