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Separable Equation Problem

  1. Sep 27, 2014 #1
    1. The problem statement, all variables and given/known data
    dx/dt=x^2+1/25,
    and find the particular solution satisfying the initial condition
    x(0)=8.

    2. Relevant equations


    3. The attempt at a solution
    So I began by taking out 1/25 from the right side, making the equation:
    dx/dt = (1/25)(25x^2 + 1)
    Then, rearranging the equation to be:
    dx/(25x^2+ 1) = (1/25) dt
    Taking the integral of both sides:
    tan^-1(5x) = (1/25) t + c
    Using the initial value x(0) = 8, I can solve for c, so first I rearrange for x.
    5x = tan( (1/25)t + c)
    x = tan ( (1/25)t + c)/5
    Plugging in 0 and 8 into the equation gives me that c = tan^-1 (40)
    However, I don't have the right answer. Can anyone help me recognize what I did wrong here? Thank you in advance.
     
  2. jcsd
  3. Sep 27, 2014 #2
    I see a mistake on the left hand side that you might spot if you do a u substitution. (u=5x, du=?)
     
  4. Sep 27, 2014 #3
    Oh, thank you, I didn't notice that. Haha, that was careless of me.
     
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