Könnte jemand bitte zeigen, wie diese DGL gelöst werden können?
Text erkannt:
(5) Solve the following systems of equations with initial data \( x(0)=x_{0}, y(0)=y_{0} \).
i) \( \left(\begin{array}{l}x \\ y\end{array}\right)^{\prime}=\left(\begin{array}{ll}2 & 0 \\ 0 & 1\end{array}\right)\left(\begin{array}{l}x \\ y\end{array}\right) \)
ii) \( \left(\begin{array}{l}x \\ y\end{array}\right)^{\prime}=\left(\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right)\left(\begin{array}{l}x \\ y\end{array}\right) \)
Moreover, draw the trajectory of the curve \( t \mapsto(x(t), y(t)) \) in the plane \( (x, y) \).
