What exactly is a 2nd order differential equation?

[Venomily]

A first order DE models the rate of change, e.g. when decay is proportional to time we have the DE: dM/dt = -K.M; this is describing that rate of change mathematically. Am I correct in saying that a 2nd order DE describes the rate of rate of change?

Also, can anyone explain any application of 2nd order DEs to me? I understand it mathematically, but I am interested in how it works in practice like that decay example I pointed out above, hence this post.

 

[D H]

Also, can anyone explain any application of 2nd order DEs to me?

Classical physics is chock full of second order ODEs. F=ma, for example.

 

[Mark44]

Classical physics is chock full of second order ODEs. F=ma, for example.

Not to mention electrical circuits with an inductor, resistor, and capacitor.

 

[Venomily]

Classical physics is chock full of second order ODEs. F=ma, for example.

Not to mention electrical circuits with an inductor, resistor, and capacitor.

Thanks, but can you go through an example with me? actually point out a real life application (which you guys did) but also deriving a 2nd order DE to model it step by step.

 

[Mark44]

Here you go - http://en.wikipedia.org/wiki/RLC_circuits

 

[HallsofIvy]

If you throw a ball directly upward with initial speed 10 m/s, the basic physics law is "force= mass times acceleration". In this case, the only force (neglecting air resistance) is gravity: -mg. Since acceleration is the second derivative of the position function, taking x to be the height above the ground at time t, we have the differential equation
$$m\frac{d^2x}{dt^2}= -mg$$
with initial conditions x(0)= 0, x'(0)= 10.