Chapter 9 - Systems of Differential Equations - 9.1 First-Order Linear Systems - True-False Review - Page 587: g

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The initial value of $x$ is $0$ at $x(0)$ while the value of $y(1)$ is $1$ at $t=1$. But from Definition 7.1.16, if all the auxiliary conditions are applied at same time $t_0$ then initial-value problem is formed. Hence, the given first-order linear system is not an initial-value problem.