Use variation of parameters to solve the given nonhomogeneous system. $$\mathbf{X}^{\prime}=\left(\begin{array}{rr} 0 & -1 \\ 1 & 0 \end{array}\right) \mathbf{X}+\left(\begin{array}{c} \sec t \\ 0 \end{array}\right)$$
Added by Juan Francisco S.
Step 1
The characteristic equation is $\det(A - \lambda I) = \lambda^2 + 1 = 0$. The eigenvalues are $\lambda = \pm i$. The eigenvectors are $\mathbf{v_1} = \begin{pmatrix} 1 \\ i \end{pmatrix}$ and $\mathbf{v_2} = \begin{pmatrix} 1 \\ -i \end{pmatrix}$. The Show moreโฆ
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