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$The solution of the DE \cos x d y = y (\sin x - y) d x, 0 < x < \frac{π}{2} is$

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tanx=(secx+c)y

secx=(tanx+c)y

ysecx=tanx+c

ytanx=secx+c

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detailed solution

Correct option is B

dydx=ytanx−y2secx⇒1y2dydx−1ytan⁡x=−sec⁡xt=1ydtdx=⋅−1y2dydx→−dtdx−tan⁡xt=−sec⁡x→dtdx+(tan⁡x)t=secx I.F. =e∫tan⁡xdx=sec⁡xtsecx=∫sec2x dxtsecx=tan⁡x+c1ysec⁡x=tan⁡x+c

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The solution of the DE cos⁡xdy=y(sin⁡x−y)dx,0<x<π2 is

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$The solution of the DE \cos x d y = y (\sin x - y) d x, 0 < x < \frac{π}{2} is$