A first order differential equation has the form,

$\frac{dx}{dt}=f(x,t),$

where $f(x,t)$ is any function of $x$ and $t$. The form below can be used to numerically integrate this equation for a total number of $N_{steps}$ steps using a step size of $\Delta t$.

Numerical 1st order differential equation solver  $ \large \frac{dx}{dt}=$ Intitial conditions:   $x(t_0)=$   $\Delta t=$ $t_0=$   $N_{steps}$

$x$
	$t$

$t$       $x$

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