Formulating a 2nd-order ODE as a system.

I am working on an assignment, and my first task is to write this second order differential equation as a system of two first order equations. I have done this previously for special cases where f and u are linear functions (typically f(u') = b*u' and s(u) = ku), but I have no idea of what to do with this generalized equation. Can somebody help me?

mu ̈+f(u ̇)+s(u)=F(t), t>0, u(0)=U0, u ̇(0)=V0

Can you please rewrite your equation? I can't read some of the symbols. They come out as gobbledy-gook.

mu'' + f(u') + s(u) = F(t) , t > 0, u(0) = U0, u'(0) = V0

The same basic procedure works. You let

Then, you can say that and

If you fill in the question mark there from the original DE, you'll be done with this step.

is y'2 = (F(t) - f(u') - s(u))/m then?

Well, it's really

with the prime on

but then you can substitute in for and right? What do you get? (No 's allowed in final answer!)

Since u = y1 and u' = y2, I get: (F(t) - f(y2) - s(y1)) / m

So writing out your system in full gives you what?