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Cramer's Rule application in differential equations

  1. Jun 2, 2012 #1
    We have this system of equations:

    [tex]
    \begin{cases}
    x'= -x + 2y & (1)\\
    y' = -2x - y + e^{-t} & (2)
    \end{cases}
    [/tex]

    where [itex]x(0) = 0 ; y(0) = 0[/itex]

    We apply the Laplace transform on (1) and (2) and get:

    [tex]
    (s + 1)X - 2Y = 0\\
    2X + (s + 1)Y = \frac{1}{s + 1}
    [/tex]

    We can use elimination here, but can we apply Cramer's Rule? We find the determinant [itex]D = (s + 1)^2 + 4[/itex], and to find [itex]X_s[/itex] and [itex]Y_s[/itex], we use a certain formula. Is this applicabale here?
     
  2. jcsd
  3. Jun 4, 2012 #2
    yes you can in fact Cramer's rule is only a shortcut to standard gaussian elimination
     
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