I need to get a single variable equation from this expression.

Question

I need some help of you guys solving the following equation:

\begin{equation} I_{D}(t)=k\cdot (1-\frac{h-\frac{1}{c}\int{dt \cdot I_{D}(t)}}{p}) \end{equation}

where $k$, $h$, $c$ and $p$ are constants and I want to get $I_{D}(t)$

Answer 1

Differentiate both sides of the equation:

$$ I_D'(t) = \dfrac{k}{cp} I_D(t)$$

which is a differential equation you should know how to solve.