We have this system of equations:(adsbygoogle = window.adsbygoogle || []).push({});

[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?

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# Cramer's Rule application in differential equations

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