Differential Equations Quiz
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SERIES AND NUMERICAL METHODS
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When using technology to implement the shooting method for the boundary value problem y′′+y=0y'' + y = 0 with y(0)=0y(0) = 0 and y(π)=0y(\pi) = 0, a student finds that the method fails to converge to a unique solution regardless of the initial guess for y′(0)y'(0). Analysis of the problem using computer algebra shows that the general solution is y=Acos⁡(x)+Bsin⁡(x)y = A\cos(x) + B\sin(x). What does this computational difficulty reveal about the boundary value problem?
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