Answer
$\dfrac{dy}{dx}=y$
and $y(0)=1$
Work Step by Step
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 $y(0)=1$
