## Calculus 10th Edition

$$y=Ce^x-8$$
$$\frac{dy}{dx}=y+8$$ Rearranging, $$\frac{dy}{y+8}=dx$$ Integrating both sides, $$\int \frac{dy}{y+8}=\int dx$$ $$ln(y+8)=x + C'$$ Taking both sides to the power of $e$, $$y+8=e^{x+C'}=e^{C'}e^x = Ce^x$$ where $C=e^{C'}$. Therefore, $$y=Ce^x-8$$