Numerical solutions of first order differential equations

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: 

$x(t_0)=$

 

$\Delta t=$

$t_0=$

 

$N_{steps}$

$x$ 

$t$

 $t$       $x$