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Variation of parameters

  • Thread starter EvLer
  • Start date
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I have been trying to get this for a while and can't figure it out:

if a fundamental matrix of the system x' = Ax is X(t)
[tex]\left(\begin{array}{cc}e^t&0\\0&e^{-t}\end{array}\right)[/tex]
find a particular solution yp(t) of [tex] x' = Ax + [e^t, 2]^{transpose}[/tex] such that yp(0) = 0

So, I got [tex]u(t) = \left(\begin{array}{cc}t&0\\0&2e^t\end{array}\right)[/tex]
but when I multiply X(t) by it, I do not get the right answer. Is there a coefficient involved with integration of u'(t)?

Thanks for help.
 

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