Consider the First-Order Nonhomogeneous Initial Value Problem

Given a Fundamental

Multiple Choice

Consider the first-order nonhomogeneous initial value problem

Given a fundamental matrix (t) for the system, what is the solution of this initial value problem?

A) $\mathbf{x}(t) =\psi(3.0) \left(\begin{array}{l}-2 \\ 4\end{array}\right) +\psi(t) \int_{3.0}^{t} \psi^{-1}(s) { }_{-5 e^{-2 s}}^{4 s^{3}+4} d s$
B) $\mathbf{x}(t) =\psi(t) \psi^{-1}(3.0) \left(\begin{array}{c}-2 \\ 4\end{array}\right) +\psi(t) \int_{3.0}^{t} \psi^{-1}(s) { }_{-5 e^{-2 s}}^{4 s^{3}+4} d s$
C) $\mathbf{x}(t) =\psi(t) \left(\begin{array}{l}-2 \\ 4\end{array}\right) +\psi(t) \int_{3.0}^{t} \psi^{-1}(s) \begin{array}{l}4 s^{3}+4 \\ -5 e^{-2 s}\end{array} s$
D) $\mathbf{x}(t) =\psi(t) \psi^{-1}(3.0) \left(\begin{array}{c}-2 \\ 4\end{array}\right) +\psi(3.0) \int_{3.0}^{t} \psi^{-1}(s) s^{3}+4 e^{-2 s} d s$