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Magazine Problem 26
Solve the initial value problems. $$f^{\prime \prime}(t)-9 f(t)=0, f(0)=0, f^{\prime}(0)=1$$
Problem 26
Solve the system with the given initial value. $$\frac{d \vec{x}}{d t}=\left[\begin{array}{ll}1 & 2 \\\3 & 0\end{array}\right] \vec{x} \text { with } \vec{x}(0)=\left[\begin{array}{l}7 \\\2\end{array}\right]$$
Problem 27
Solve the initial value problems. $$f^{\prime \prime}(t)+9 f(t)=0, f(0)=0, f\left(\frac{\pi}{2}\right)=1$$
Problem 27
Solve the system with the given initial value. $$\frac{d \vec{x}}{d t}=\left[\begin{array}{rr}-4 & 3 \\\2 & -3\end{array}\right] \vec{x} \text { with } \vec{x}(0)=\left[\begin{array}{l}1 \\\0\end{array}\right]$$
Problem 28
Solve the system with the given initial value. $$\frac{d \vec{x}}{d t}=\left[\begin{array}{ll}4 & 3 \\\4 & 8\end{array}\right] \vec{x} \text { with } \vec{x}(0)=\left[\begin{array}{l}1 \\\1\end{array}\right]$$
Problem 28
Solve the initial value problems. $$f^{\prime \prime}(t)+f^{\prime}(t)-12 f(t)=0, f(0)=f^{\prime}(0)=0$$
Problem 28
Find all real solutions of the systems in Exercises 27 through 30 $$\frac{d \vec{x}}{d t}=\left[\begin{array}{rr} 0 & 4 \\ -9 & 0 \end{array}\right] \vec{x}$$
Problem 29
Solve the initial value problems. $$f^{\prime \prime}(t)+4 f(t)=\sin (t), f(0)=f^{\prime}(0)=0$$
Problem 29
Solve the system with the given initial value. $$\frac{d \vec{x}}{d t}=\left[\begin{array}{ll}1 & 2 \\\2 & 4\end{array}\right] \vec{x} \text { with } \vec{x}(0)=\left[\begin{array}{l}5 \\\0\end{array}\right]$$
Problem 30
Solve the system with the given initial value. $$\frac{d \vec{x}}{d t}=\left[\begin{array}{ll}1 & 2 \\\2 & 4\end{array}\right] \vec{x} \text { with } \vec{x}(0)=\left[\begin{array}{r}2 \\\\-1\end{array}\right]$$
