I dont know if this Counts as a differential equation, but here it is. $\displaystyle \int_0^d \frac{\partial E}{\partial x}dx=E_0$. The condition is that $\displaystyle \frac{\partial E}{\partial x}>0$ in the interval [0,d] and that $\displaystyle E(0)=0$ and $\displaystyle E(d)=E_0$. I can see that a solution is $\displaystyle E=xE_0 /d$ but I dont know how to find this without guessing. Is there a simple method to employ?