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    Cauchy differential equation

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    Prove d/dt(u(x(t),t))+tanh(x(t))(d/dx(u(x(t),t)))=0
    u(x(t),0)=a(x(t))
    limit as x tends to infinity of u(x,t)=0

    has at most one solution.Explain why there is no boundary condition at x=0
    and find a solution for the special case a(x(t))=sinh(x(t))

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    https://brainmass.com/math/partial-differential-equations/cauchy-partial-differential-equation-82837

    Solution Summary

    This shows why a given differential equation has at most one solution.

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