solve: (sin^2 (x)−y)dx−tan(x)dy=0


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Question Number 103089 by M±th+et+s last updated on 12/Jul/20

$s o l v e :$ $({s i n}^{2} (x) - y) d x - t a n (x) d y = 0$
	Answered by Ar Brandon last updated on 12/Jul/20
	$⇒{tanx(dy/dx)+y=sin^2 x}∙cosx ⇒sinx(dy/dx)+ycosx=sin^2 xcosx ⇒(d/dx)(ysinx)=sin^2 xcosx ⇒ysinx=∫sin^2 xcosxdx=((sin^3 x)/3)+C ⇒y=((sin^2 x)/3)+(C/(sinx))$
	$\Rightarrow {tanx \frac{dy}{dx} + y = \sin^{2} x} \cdot cosx$ $\Rightarrow sinx \frac{dy}{dx} + ycosx = \sin^{2} xcosx$ $\Rightarrow \frac{d}{dx} (ysinx) = \sin^{2} xcosx$ $\Rightarrow ysinx = \int \sin^{2} xcosxdx = \frac{\sin^{3} x}{3} + C$ $\Rightarrow y = \frac{\sin^{2} x}{3} + \frac{C}{sinx}$
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