Learning DEs: Solving 2nd Order Differential Equations

[greg_rack]

Hi guys,

I have just started studying DEs on my own, so pardonne moi in advance for the probably silly question :)

Via Newton's second law of motion:
$$x''=\frac{F}{m} \ [1]$$
Which is a second-order differential equation.
But, from here, how do I get the good old equation of motion:
$$x(t)=\frac{F}{2m}t^2+vt+x$$
by solving the DE? What is the procedure to apply? In my textbook, only second-order homogeneous DE are treated, but nothing with the form of $[1]$... and online everything looks over-complicated.

 

[greg_rack]

Ok, I managed to get to the solution just by integrating twice both sides.
I was wrapping my head for nothing!