## University Calculus: Early Transcendentals (3rd Edition)

$\dfrac{dy}{dx}=y$ and $y(0)=1$
In order to determine the differential equation, we will have to take the derivative of the differential equation. Here, we have: $\dfrac{dy}{dx}=0+y(x)$ or, $\dfrac{dy}{dx}=y$ Apply the initial conditions: Then, we have $y(0)=1$ Hence, our answers are: $\dfrac{dy}{dx}=y$ and $y(0)=1$