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Let y = y(x) satisfy dy/dx = (tan x - y)*sec² x on x in (-pi/2, pi/2) with y(0) = 0. If y(-pi/4) = e - k, find the value of k.
- 2
- 1
- 0
- 3
Correct answer: 2
Solution
Solving the linear ODE gives y = tan x - 1 + e^(-tan x); at x = -pi/4, y = -2 + e = e - 2, so k = 2.
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