Solved

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

Question 19

Multiple Choice

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

Multiple Choice

Correct Answer:VerifiedUnlock this answer nowGet Access to more Verified Answers free of chargeAccess For Free

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

Correct Answer:
Verified
Unlock this answer now
Get Access to more Verified Answers free of charge