Find the particular solution for $A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$, $\vec{g}(t) = \begin{bmatrix} 2\sin(t) + \cos(t) \\ -5\sin(t) + 3\cos(t) \end{bmatrix}$
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Since $A = I$, the homogeneous solution is $\vec{x}_h(t) = c_1e^t\begin{bmatrix} 1 \\ 0 \end{bmatrix} + c_2e^t\begin{bmatrix} 0 \\ 1 \end{bmatrix}$. The particular solution is of the form $\vec{x}_p(t) = \begin{bmatrix} a\sin(t) + b\cos(t) \\ c\sin(t) + d\cos(t) Show more…
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