Having trouble with differential equations and separation of variables

1. Apr 20, 2004

cair0

two problems in particular, one i got in calc, the other in physics

one asks if $$a = -v$$
and $$v = 1$$ when $$t = 0$$
what is a possible position function for this equation

the other one is
given $$a = 3x$$
and starting at rest from $$x = 0$$
find the velocity at 5 seconds

i cant seem to get the concept behind these, because the times we do them are so far and few between

2. Apr 21, 2004

gnome

For the first one:

since a = dv/dt = -v, you could solve it as a separable equation by writing it as
dv/v = -dt
and integrating both sides.

But you should really be able to do this one just by inspection.

Start off by thinking of a function that is equal to its own derivative & then think of how you can modify it to be equal to the negative of its derivative.

If you need more of a clue, look at the last item on this page:
(I can't understand why chroot didn't like it; I loved it. )

Then give it a constant coefficient C and use the given boundary condition v(0) = 1 to find the value of C.

3. Apr 21, 2004

HallsofIvy

Staff Emeritus
I started to do some complicated calculations on the second question when suddenly it hit me: the objects acceleration is proportional to x and x= 0??? And its initial speed is also 0?? What does that tell you?

4. Apr 21, 2004

cair0

the assumption is that it will accelerate...

5. Apr 21, 2004

cair0

yeah that one was really obvious now that i think about it, for some reason i kept getting stuck with the 2nd derrivative of x = the 1st derivative of x, and that notation ws getting me nowhere...