# Ballistics differential equations

## Main Question or Discussion Point

i have wandered past my math background into drag equations on bullets. i found the equation that relates acceleration and speed of the bullet. I do not know how to integrate multi-varible equations. How to i get the equation so it can be graphed on an acceleration vs time? I am thinking from there i can integrate again to velocity vs time then again to displacement vs time. I am not really interested in learning how to do this right now, since i will learn it in class later, i just need the answer to complete my program. The equation i have is
a=(D*V^2*B*A)/(2*M)

D=air density
V=velocity
B=ballistic coefficient
A=cross sectional area
M=mass

HallsofIvy
Homework Helper
So you have
$$\frac{dv}{dt}= \frac{DBA}{2M}v^2$$

That seperates as
$$\frac{dv}{v^2}= \frac{DBA}{2M}dt$$

which can be integrated to
$$-\frac{1}{v}= \frac{DBA}{2M}t+ C$$
where C is a constant of integration.