# 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...