The solution of the D.E $$2x2ydydx=$$$$tan$$⁡$$x2y2$$−$$2xy2$$, given that $$y(1)=$$π$$2$$ is

Correct option is 4sin(x2y2)=ex-1

Questions

$The solution of the D.E 2 x^{2} y \frac{dy}{dx} = \tan (x^{2} y^{2}) - 2 {xy}^{2}, given that y (1) = \sqrt{\frac{π}{2}} is$

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sin(x2y2)=ex+1

sin(x2y2)=x

cos(x2y2)+x=0

sin(x2y2)=ex-1

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detailed solution

Correct option is D

we know ddxx2y2=x22ydy dx+y2 2xGiven equation 2x2ydydx+2xy2=tan(x2y2) ddxx2y2=tan⁡x2y2⇒∫cot⁡x2y2dx2y2=∫dx⇒log⁡sinx2y2=x+C Put x=1,y=π2 log sinπ2=1+C 0=1+C then C=−1log⁡sinx2y2=x-1sin⁡x2y2=ex−1

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The solution of the D.E 2x2ydydx=tan⁡x2y2−2xy2, given that y(1)=π2 is

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Ready to Test Your Skills?

free study material

$The solution of the D.E 2 x^{2} y \frac{dy}{dx} = \tan (x^{2} y^{2}) - 2 {xy}^{2}, given that y (1) = \sqrt{\frac{π}{2}} is$