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Q.

The acute angle between the two line passing through the origin and satisfying the differential  equation (4x−3y)dx+(2y−3x)dy=0

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a

θ=tan−113

b

θ=tan−123

c

θ=π2

d

θ=00

answer is A.

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Detailed Solution

4xdx+2ydy−3ydx+xdy=04xdx+2ydy−3d(xy)=02x2+y2-3xy=c(0,0)⇒c=0 hence (x−y)(2x−y)=0θ=tan−113     since tanθ=m1-m21+m1m2
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