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Calculus: separable differential equations

  1. Feb 5, 2008 #1
    1. The problem statement, all variables and given/known data
    The question is discussing the growth rate of a tumor as it decreases in size (called the Gompertz equation: I am needing so SOLVE THE SEPERABLE DIFFERENTIAL EQUATION.

    2. Relevant equations
    dx/dt = f(t)g(x) =(e^-t)(x(t)) x(o)=1

    3. The attempt at a solution

    1. im separating variables, (i think im making a mistake here)
    .. is that step right?

    2. then i integrate both sides.

    integrating 1/x(t) on one side.. and integrating e^-t(dt) on the other.. i get
    ln|x|= -e^-t + c
    .. now im unsure as to how to solve the rest. am i solving for a variable for c?
  2. jcsd
  3. Feb 6, 2008 #2


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    Staff Emeritus
    Science Advisor

    Looks to me like you have done everything right. Now use the fact that x(0)= 1 to find c. ln|1|= 0= -e^0+ c or 0= -1+ c. What is c? (c isn't, technically, a "variable", it is constant.)
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