Discrete Integrator instead of Continuous Integrator

Hi! I am trying to Model control for a Micro-controller which (under Real Time Development) does not support Continuous time solver. So, instead i have to use Discrete Time Solver. How do i replace SECOND ORDER INTEGRATOR with DISCRETE TIME INTEGRATOR? The equation i am modelling is a Second Differential Equation.

Equation: m.y" = F_coil - Ks.x -mg

where

y" = d^2(x)/dt

F_coil = ((ni)^2)/(2.g^2)

{ where n=number of turns

i=current

g=air gap

Ks = Spring Pre-load

x = distance travelled by the solenoid plunger }

m = mass of the plunger

g = gravitational constant

Intentionally this is easy using a second order integrator. BUT HOW DO I ACHIEVE THE SAME WITH DISCRETE TIME INTEGRATOR?

I am grateful for any input!!