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    Differential Equation and Matrix Determinant : The ODE X"+ kX = 0 has different types solution depending on sign of k....

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    1.The ODE X"+ kX = 0 has different types solution depending on sign of k.
    We consider the three possible cases separately.
    k=0: X"=0 so that X(x)=Ao+Box, X'(0)=0 implies Bo=0 so that X(x)=Ao. Finally, X(1)=0 implies Ao=0 and there is only trivial solution X=0.

    The matrix has determinant e^mu + e^-mu= 2cosh.mu, which is never zero and it follows that pair of equations has unique solution Ahat=Bhat=0 and only trivial solution X=0.
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    © BrainMass Inc. brainmass.com October 9, 2019, 5:32 pm ad1c9bdddf
    https://brainmass.com/math/matrices/differential-equation-matrix-determinant-60104

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    A differential equation and a matrix determinant are investigated.

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