I think I know how to solve(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{d\vec{x}}{dt}= A \vec{x}[/tex]

where A is a constant nXn matrix. We just compute the eigenvalues and the corresponding eigenvectors.

But how do we solve

[tex]\frac{d^2\vec{x}}{dt^2}= A \vec{x}[/tex]

Can we say straight away that the solution is (following that of one dependent variable)

[tex]\vec{x}(t) = exp(-Mt) \vec{x}_1+ exp(Mt) \vec{x}_2 [/tex]

where M^{2}=A and x_{1}and x_{2}are constant vectors.

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# System of linear second order differential equations

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