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Having trouble with differential equations and separation of variables

  1. Apr 20, 2004 #1
    two problems in particular, one i got in calc, the other in physics

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

    the other one is
    given [tex] a = 3x [/tex]
    and starting at rest from [tex]x = 0[/tex]
    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. jcsd
  3. Apr 21, 2004 #2
    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. :biggrin: )

    Then give it a constant coefficient C and use the given boundary condition v(0) = 1 to find the value of C.
  4. Apr 21, 2004 #3


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    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?
  5. Apr 21, 2004 #4

    the assumption is that it will accelerate...
  6. Apr 21, 2004 #5

    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...
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