QuestionShow that the system $\mathbf{y}^{\prime}=A \mathbf{y}$ can be solved directly for a $2 \times 2$ upper triangular matrix $A$ with constant entries. Use the form $\left[\begin{array}{l} x \\ y \end{array}\right]^{\prime}=\left[\begin{array}{ll} a & b \\ 0 & c \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\right]$ and solve the second equation first.

Studdy Solution
Finally, solve for $x$ by dividing both sides by $e^{at}$ .
$x = \frac{bC}{a+c}e^{ct} + C5e^{-at}$ The solution to the system of equations is given by $\left[\begin{array}{l}x \\y\end{array}\right] = \left[\begin{array}{l}\frac{bC}{a+c}e^{ct} + C5e^{-at} \\Ce^{ct}\end{array}\right]$

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