The solution of differential equation xdx−ydyxdy−$$ydx=1+x2$$−$$y2x2$$−$$y2$$ is

Correct option is 3x2−y2+1+x2−y2=cx+yx2−y2

Questions

$The solution of differential equation \frac{x d x - y d y}{x d y - y d x} = \sqrt{\frac{1 + x^{2} - y^{2}}{x^{2} - y^{2}}} is$

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x2−y2+x−y+C

x2−y2+x2+y2+C

x2−y2+1+x2−y2=cx+yx2−y2

x2−y2+1+x2−y2=cx−yx2+y2

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detailed solution

Correct option is C

Put x=rsec⁡θ y=rtan⁡θ⇒drsec⁡θdθ=1+r2∫dr1+r2=∫sec⁡θdθln⁡r+1+r2=ln⁡|sec⁡θ+tan⁡θ|+ln⁡|c|⇒x2−y2+1+x2−y2=∣c(x+y)x2−y2

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The solution of differential equation xdx−ydyxdy−ydx=1+x2−y2x2−y2 is

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$The solution of differential equation \frac{x d x - y d y}{x d y - y d x} = \sqrt{\frac{1 + x^{2} - y^{2}}{x^{2} - y^{2}}} is$