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Seperable DE with Initial Condition

  1. Jan 24, 2014 #1
    1. The problem statement, all variables and given/known data
    dy/dx =4yx^3-y y(1)=-3
    dy/y = (4x^3-1)dx
    ln(y) = x^4-x+C
    y = e^(x^4-x+C)

    But an answer source says that after the integration I get
    ln(y) = x^4 - x + ln(C)
    so then..
    ln(y/c) = x^4 - x
    y = Ce^(x^4 - x)

    which makes it much easier to solve for the constant given the initial condition... My question is why when you take the integral is the constant ln(C) instead of just C...?
  2. jcsd
  3. Jan 24, 2014 #2
    It's really the same thing, but it makes the final result look simpler. The two things are equivalent.
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