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Q.

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

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a

x2−y2+x−y+C

b

x2−y2+x2+y2+C

c

x2−y2+1+x2−y2=cx+yx2−y2

d

x2−y2+1+x2−y2=cx−yx2+y2

answer is C.

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Detailed Solution

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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