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Simple differential equation

  1. Nov 1, 2008 #1
    1. The problem statement, all variables and given/known data

    How would you solve


    Thanks for your help
  2. jcsd
  3. Nov 1, 2008 #2


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    Homework Helper

    Try rearranging the equation.

    [tex]\int{v_{(t)} = 4 - \frac{v_{(t)}}{5}[/tex]

    What function do you know that will yield this kind of result?
  4. Nov 2, 2008 #3
    I know the answer is 20e^(-5t) by just taking the 1/10 out from the v(t), and the k on top of the exponential is negative 10/2 but I don't know the solving mechanism

    My calc book only has one example and it is when it equals a function and not a constant in the first equation, so I can just differentiate the equation to get rid of the integral

    The answer should be in the form A+Bexp(-kt)
    A is zero for this equation but can I find B without any initial conditions?
  5. Nov 2, 2008 #4


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    Homework Helper

    [tex]\int{v_{(t)} = 4 - \frac{v_{(t)}}{5}[/tex]

    Taking the common integral of e you can start with this

    [tex]\int{e^{(ct)} = \frac{e^{ct}}{c}[/tex]

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