1. a) Find a general solution p(x) of y - 2ay' + ay = 0. b)...

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1. a) Find a general solution p(x) of y" - 2ay' + a²y = 0. b) Find a general solution (x) of y" - 2ay' + (a²-82)y = 0 in which e is a positive constant c) Show that, as → 0, the solution in b) does not approach the solution in (a), even though the differential equation in (b) would appear to approach the equation in (a). This shows how small changes in the coefficients of a differential equation may cause significant changes in the solution. 1. a) Find a general solution p(x) of y" - 2ay' + a²y = 0. b) Find a general solution (x) of y" - 2ay' + (a²-82)y = 0 in which e is a positive constant c) Show that, as → 0, the solution in b) does not approach the solution in (a), even though the differential equation in (b) would appear to approach the equation in (a). This shows how small changes in the coefficients of a differential equation may cause significant changes in the solution.

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a The general solution x of the differential equation y 2ay a2y 0 is given by x c1eax c2eax where c1 ... View the full answer