Question

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. The equation of the curve is

(a) sin(y/x) = log x + (1/2) 

(b) cosec(y/x) = log x + 2

(c) sec(2y/x) = log x + 2

(d) cos(2y/x) = log x + (1/2)  

Answer 1

Answer is (a) sin(y/x) = log x + (1/2)

Explanation:

Given dy/dx = (y/x) + sec(y/x) ...(i)

which is a homogeneous differential equation.

Let y = vx 

dy/dx = v + x(dv/dx)

which is passing through (1,π/6), 

so, c = 1/2 

Hence, the equation of the curve is

sin(y/x) = log |x| + (1/2)