The solution of $$dydx+2ytanx=$$$$sin$$⁡x , given that $$y=0$$,$$x=$$π$$/3$$ is

Correct option is 1y=cosx-2cos2x

Questions

$The solution of \frac{d y}{d x} + 2 y t a n x = \sin x, given that y = 0, x = π / 3 is$

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y=cosx-2cos2x

y=cosx+2cos2x

y=cosx-cos2x

y=2cosx-2cos2x

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detailed solution

Correct option is A

I.F=e∫2ttax⁡dx=e2log⁡|sec⁡x|=sec2⁡x Solution of the differential equation is ysec2⁡x==∫sin⁡xcos2⁡xdx=∫sec⁡xtan⁡xdx=sec⁡x+c If x=π/3→4y=2+cy=0⇒c=−2⇒ysec2x=secx−2y=cos⁡x−2cos2⁡x

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The solution of dydx+2ytanx=sin⁡x , given that y=0,x=π/3 is

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$The solution of \frac{d y}{d x} + 2 y t a n x = \sin x, given that y = 0, x = π / 3 is$