A curve passes through the point 1 , π 6 . Let the slope of the curve at each point x , y be y x + sec y x , x > 0 . Then the equation of the curve is

Step-by-step solution

Given slope at (x, y) is dy dx = y x + sec y x ...... i let y x = t ⇒ y = xt Differentiating this wrt x ⇒ dy dx = t + x dt dx ...... i i Now using equation i and i i , we have t + x dt dx = t + sec t ⇒ d t sec t = d x x Integrating both sides. ∫ cos t dt = ∫ 1 x dx sin t = ln x + c Now Put value of t in above equation. sin y x = ln x + c ..... i i i Given that curve passes through 1 ,  π 6 so put in above equation. sin π 6 = ln 1 + c ⇒ c = 1 2 Now, put the value of