Cramer's Rule application in differential equations

[Hiche]

We have this system of equations:

<br /> \begin{cases}<br /> x&#039;= -x + 2y &amp; (1)\\<br /> y&#039; = -2x - y + e^{-t} &amp; (2)<br /> \end{cases}<br />

where x(0) = 0 ; y(0) = 0

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

<br /> (s + 1)X - 2Y = 0\\<br /> 2X + (s + 1)Y = \frac{1}{s + 1}<br />

We can use elimination here, but can we apply Cramer's Rule? We find the determinant D = (s + 1)^2 + 4, and to find X_s and Y_s, we use a certain formula. Is this applicabale here?

 

[charbel]

yes you can in fact Cramer's rule is only a shortcut to standard gaussian elimination