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    Differential Equation : Find General Solution

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    Find a general solution on (-pi/2, pi/2) to y'' + y = tan x given that S secx dx = ln |sec x + tan x|.

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    Please see the attached file for the complete solution.

    (i) This equation is in the standard form: y'' + y = tanx

    (ii) The associated homogenous equation is y'' + y = 0
    The characteristic equation is: λ2 + 1 = 0
    λ1 = i and λ2 = -i
    yh = c1 cos x + c2 sin x
    y1 = cos x, y2 = sin x, g(x) = tanx
    y1' = -sin x, y2' = cos x


    (vi) yp = u1y1 + u2y2 = cos x(sin x - ln (secx + tanx)) - sin x cos x
    = -cos x ...

    Solution Summary

    A general solution is found to a differential equation. The solution is detailed and well-presented.