Question

If dy/dx + 2y tan x = sin x and if y = 0 when x = π/3 express y in terms of x

Answer 1

dy/dx + 2y tan x = sin x

Here P = 2 tan x and Q = sin x

∫P dx = ∫2 tan x = 2 log sec x = log sec² x

I.F = e^\(\int\)pdx = e^{log sec^2 x} = sec²x

C = -Sec π/3 = -2

The solution is y sec² x = sec x – 2