​ If y = y(x), y ∈ [0, π/2) is the solution of the differential equation ​sec y dy/dx - sin(x+y) = 0 with y (0), then 5y' (π/2) is equal to

Question

If y = y(x), y ∈ [0, \(\frac{\pi}{2}\)) is the solution of the differential equation

sec y \(\frac{dy}{dx}\) - sin(x+y) - sin (x-y) = 0 with y(0) = 0, then 5y'\(\left(\frac{\pi}{2} \right)\) is equal to ............ .

Answer 1

Correct answer 2

sec y \(\frac{dy}{dx}\) = 2 sinx cosy

sec² ydy 2sin xdx 

tany = - 2cosx + c 

c = 2 

tany = –2cosx + 2 \(\Rightarrow\) at x = \(\frac{\pi}{2}\)

tan y = 2

sec² y\(\frac{dy}{dx}\)  = 2sin x

5\(\frac{dy}{dx} = 2\)