Consider the first-order nonhomogeneous system of linear differential equations Where the components of g(t) are continuous functions.Given a fundamental matrix (t) for the system, what is the solution of this system if it is equipped with the initial condition x(3.6) = X ₀? A) $ x(t)=\psi(0) \mathbf{x}_{0}+\psi(t) \int_{0}^{t} \psi^{-1}(s) \mathbf{g}(s) d s $ B) $ x(t)=\psi(t) \psi^{-1}(3.6) \mathbf{x}_{0}+\psi(t) \int_{3.6}^{t} \psi^{-1}(s) g(s) d s $ C) $ x(t)=\psi(3.6) \mathbf{x}_{0}+\psi(t) \int_{3.6}^{t} \psi^{-1}(s) \mathbf{g}(s) d s $ D) $ x(t)=\psi(t) \psi^{-1}(0) \mathbf{x}_{0}+\psi(t) \int_{0}^{t} \psi^{-1}(s) g(s) d s $

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The Answer of Consider the first-order nonhomogeneous system of linear differential equations Where the components of g(t) are continuous functions.Given a fundamental matrix (t) for the system, what is the solution of this system if it is equipped with the initial condition x(3.6) = X ₀? A) $ x(t)=\psi(0) \mathbf{x}_{0}+\psi(t) \int_{0}^{t} \psi^{-1}(s) \mathbf{g}(s) d s $ B) $ x(t)=\psi(t) \psi^{-1}(3.6) \mathbf{x}_{0}+\psi(t) \int_{3.6}^{t} \psi^{-1}(s) g(s) d s $ C) $ x(t)=\psi(3.6) \mathbf{x}_{0}+\psi(t) \int_{3.6}^{t} \psi^{-1}(s) \mathbf{g}(s) d s $ D) $ x(t)=\psi(t) \psi^{-1}(0) \mathbf{x}_{0}+\psi(t) \int_{0}^{t} \psi^{-1}(s) g(s) d s $

Consider the First-Order Nonhomogeneous System of Linear Differential Equations x(t)=ψ(0)x0+ψ(t)∫0tψ−1(s)g(s)ds x(t)=\psi(0) \mathbf{x}_{0}+\psi(t) \int_{0}^{t} \psi^{-1}(s) \mathbf{g}(s) d s x(t)=ψ(0)x0​+ψ(t)∫0t​ψ−1(s)g(s)ds

Consider the First-Order Nonhomogeneous System of Linear Differential Equations
$x(t)=\psi(0) \mathbf{x}_{0}+\psi(t) \int_{0}^{t} \psi^{-1}(s) \mathbf{g}(s) d s$