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If y = y(x) is the solution of the differential equation dy/dx = (tan x - y) sec² x, x ∈ (-π/2, π/2) such that y(0) = 0, then y(-π/4) is equal to:
- 1/2 - e
- e - 2
- 2 + 1/e
- 1/e - 2
Correct answer: e - 2
Solution
The correct option is derived from solving the given first-order linear differential equation using an integrating factor. By applying the initial condition y(0) = 0, we can find the particular solution and evaluate it at x = -π/4, leading to the result e - 2.
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