Answer:
Option A
Explanation:
Concept involved
solving of homogeneous differential equation i.e, substitute yx=v
∴ y=vx
dydx=v+xdvdx
here, slope of the curve at (x, y) is
dydx=yx+sec(yx)
put yx=v
∴ v+xdvdx=v+sec(v)
⇒ xdvdx=sec(v)
⇒ ∫dvsecv=∫dxx
⇒ ∫cosvdv=∫dxx
⇒ sinv=logx+logc
⇒ sin(yx)=log(cx)
as it passes through (1,π6)
⇒ sin(π6)=logc
⇒logc=12
∴ sin(yx)=logx+12