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# Existence an duniqueness

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Using the existence-uniqueness theorem show that the following IVP has a solution but it is not unique:

y''+y'/x-9y/x^2=0

y(0) bounded

general solution: y=Ax^3+Bx^{-3}

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This provides an example of working an existence and uniqueness proof.

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The uniqueness and existence theorem states that

Let p(t), q(t), and g(t) be continuous on [a,b], then the differential equation

y'' + p(t)y' + q(t)y = g(t) y(t0) = y0 y'(t0) = y'0

has a ...

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