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    Wronskian property

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    Suppose that y1, y2 are linearly independent solutions to the differential equation:
    a2 (x) y'' + a1 (x) y' + a0 (x) y = 0.

    a) Show that a2 (y1 y2'' - y2 y1'') + a1(y1 y2' - y1' y2) = 0
    b) show that (a) implies a2 W' + a1 W = 0 {here W means the Wronskian)
    c) show that the equation in (b) implies W = C e(-(a1/ a2)x)

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    Solution Summary

    This shows how to prove a given Wronskian property for a differential equation. The linearly independent solution to the differential equation is discussed.