The general solution of $$dydx=2ytan$$⁡$$x+tan2$$⁡x is

Correct option is 1ycos2x=x2-14sin2x+c

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$The general solution of \frac{d y}{d x} = 2 y \tan x + \tan^{2} x is$

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ycos2x=x2-14sin2x+c

ysin2x=x2-cos2x4+c

ycos2x=x4-12sin2x+c

ysin2x=x4-12cos2x+c

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detailed solution

Correct option is A

dydx=2ysinxcosx+sin2xcos2x cos2⁡xdydx−ysin2x=sin2⁡x→dcos2⁡x⋅y=sin2⁡x=12(1−cos⁡2x) ∫dcos2⁡x⋅y=12∫1dx−∫cos⁡2x dx⇒ycos2x=x2−14sin⁡2x+c

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The general solution of dydx=2ytan⁡x+tan2⁡x is

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$The general solution of \frac{d y}{d x} = 2 y \tan x + \tan^{2} x is$