Chapter 6 - Differential Equations - 6.1 Exercises - Page 404: 52

$y=-10e^{-\frac{x}{2}} +C$

Use separation of variables, then integrate the differential equation. $\frac{dy}{dx}= 5e^{-\frac{x}{2}} $ $\int dy= \int 5e^{-\frac{x}{2}} dx$ Use u-substitution let $ u=-\frac{x}{2}$ then $du= -\frac{1}{2} dx$ $y=-10\int e^u du$ $y= -10e^{-\frac{x}{2}} +C$