Question
Solve the following initial value problems. (Show the details.)$$\begin{array}{l}y_{1}^{\prime}=y_{2}+2 y_{2} \\y_{2}^{\prime}=\frac{1}{2} y_{1}+y_{2} \\y_{2}(0)=16, y_{2}(0)=-2\end{array}$$
Step 1
We have: $$\begin{pmatrix} y_{1}^{\prime} \\ y_{2}^{\prime} \end{pmatrix} = \begin{pmatrix} 0 & 1 \\ 1/2 & 1 \end{pmatrix} \begin{pmatrix} y_{1} \\ y_{2} \end{pmatrix} + \begin{pmatrix} 2y_{2} \\ 0 \end{pmatrix}$$ Show more…
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