In the equations
$$\mathbf{F} = \mathbf{-\mathit{e}(E + v \times B)} = m\frac{d\mathbf{v}}{dt}$$ $$\frac{d^2x}{dt^2}= -\frac{e}{m}\left(E_x + B_z\frac{dy}{dt}- B_y \frac{dz}{dt}\right)$$ $$\frac{d^2y}{dt^2}=-\frac{e}{m}\left(E_y+B_x\frac{dz}{dt}-B_z\frac{dx}{dt}\right)$$ $$\frac{d^2z}{dt^2}=-\frac{e}{m}\left(E_z+B_y\frac{dx}{dt}-B_x\frac{dy}{dt}\right)$$
Is it correct to use $d$ or should I use $\partial$?
(Reference for equations: Liao, Samuel Y. Microwave Devices and Circuits. Englewood Cliffs, NJ: Prentice-Hall, 1980. Print. Page 12.)
Here $x$, $y$ and $z$ appear to be functions of only the one variable $t$ (representing, I suppose, the coordinates of a particle at time $t$). There is no other variable in sight, and you're certainly not taking derivatives with respect to any other variable. So $d$ is correct.