Chapter 9 - Differential Equations - 9.3 Separable Equations - 9.3 Exercises - Page 645: 10

$z=-t$

$\frac{dz}{dt}+e^{t+z}=0$ $\frac{dz}{dt}=-e^{t+z}$ $\frac{dz}{dt}=-e^{t}e^{z}$ $\frac{1}{e^{z}}dz=-e^{t}dt$ $\int \frac{1}{e^{z}}dz=\int -e^{t}dt$ $\int e^{-z}dz=\int -e^{t}dt$ $-e^{-z}=-e^{t}$ $e^{-z}=e^{t}$ $-z=t$ $z=-t$