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Question Number 43008 by MJS last updated on 06/Sep/18

$${\left(y^{\prime }\right)}^2=-1+\sin x$$$$y=?$$

Answered by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18

$$\frac{dy}{dx}=\sqrt{-1+sinx}$$$$\frac{dy}{dx}=\sqrt{-1(1-sinx)}$$$$\frac{dy}{dx}=i\sqrt{{sin}^2\frac{x}{2}-2sin\frac{x}{2}cos\frac{x}{2}+{cos}^2\frac{x}{2}}$$$$\frac{dy}{dx}=i(sin\frac{x}{2}-cos\frac{x}{2})$$$$dy=i(sin\frac{x}{2}-cos\frac{x}{2})dx$$$$y=i(-2cos\frac{x}{2}-2sin\frac{x}{2})+c\leftarrow ans$$$$recheck$$$$y=-2i(cos\frac{x}{2}+sin\frac{x}{2})$$$$\frac{dy}{dx}=-2i(-\frac{1}{2}sin\frac{x}{2}+\frac{1}{2}cos\frac{x}{2})$$$$\frac{dy}{dx}=i(sin\frac{x}{2}-cos\frac{x}{2})$$$${\left(\frac{dy}{dx}\right)}^2=-1(1-sinx)$$$${\left(\frac{dy}{dx}\right)}^2=(-1+sinx)$$$$isitrightorwrongplscheck...$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

Commented by abdo.msup.com last updated on 06/Sep/18

$$itsclearthatyisacomplexfunction$$$$youansweriscorrectyouhaveverifying$$$$this.$$

Commented by tanmay.chaudhury50@gmail.com last updated on 06/Sep/18

$$thankyousir...$$

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