Determine the solution to the initial value problem: dp/dt = 2p(t) + q(t) dq/dt = p(t) + 2q(t) with initial conditions p(0) = 1 and q(0) = 3.
Added by Cathy C.
Step 1
Let \(\mathbf{y}(t) = \begin{pmatrix} p(t) \\ q(t) \end{pmatrix}\). The system can be written as: \[ \frac{d\mathbf{y}}{dt} = \mathbf{A} \mathbf{y} \] where \(\mathbf{A} = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}\). Show more…
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