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Question

Solve the differential equation:
dydx+ytanx=cos3x

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Solution

dydx+ytanx=cos3x
Here p=tanx,q=cos3x
Integrating factor =epdx=etanxdx=eln(secx)=secx
Therefore,
Solution of the equation is-
y(I.F.)=q×I.F.dx
ysecx=cos3xsecxdx
ysecx=cos2xdx
ysecx =(1+cos2x2)dx(cos2x=2cos2x1)
y=xcosx2+14sin2xcosx+Ccosx

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