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Given dy/dx + (3/cos² x)*y = 1/cos² x for x in (-pi/3, pi/3), with y(pi/4) = 4/3, find the value of y(-pi/4).
- 1/3 + e⁶
- 1/3
- -4/3
- 1/3 + e³
Correct answer: 1/3 + e⁶
Solution
With IF = e^(3 tan x), the solution is y = 1/3 + C*e^(-3 tan x). Using y(pi/4) = 4/3 gives C = e³, so y(-pi/4) = 1/3 + e³*e³ = 1/3 + e⁶.
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