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A curve passes through the point (1,π/6) . Let the slope of the curve at each point (x,y) be yx+sec⁡(y/x),x>0 then the equation of the curve is

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a

siny/x=logx+12

b

cosecy/x=logx+2

c

sec2y/x=logx+2

d

cos2y/x=logx+12

answer is A.

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Detailed Solution

dydx=yx+sec⁡(y/x) put y=vxv+xdvdx=v+secv→dv secv =dxx→∫cosvdv=∫dxx→sin⁡(y/x)=ln⁡x+c The curve passes through (1,π/6) is →12=c→sin⁡(y/x)=ln⁡x+12

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A curve passes through the point (1,π/6) . Let the slope of the curve at each point (x,y) be yx+sec⁡(y/x),x>0 then the equation of the curve is