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

False

The system of differential equations $x′=ty+5(\sin t)y-3e^t$, Because it is in form $\frac{dx_1}{dt}=a_{11}(t)x_1(t)+a_{12}(t)x_2(t)+...+a_{1n}(t)x_n(t)+b_1(t)$ where $a_{ij}(t)$ and $b_i(t)$ are specified functions on an interval $I$. But $y′ =t^2x-7xy-1$ is not a first-order linear system of differential equations because a term $7x$ is not linear.