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Need explanation of this differential equation

  1. Oct 14, 2012 #1
    I need explanations at the last part of this math solution.

    Solve the differential equation:
    y' = (1 + 2/x)y

    ln|y| = x+ln(x^2)+c

    |y| = e^c.x^2.e^x

    y = Cx^2.e^x (C = +/-e^c is any constant that is not equals to 0)

    What I don't understand is this part where : |y| = e^c.x^2.e^x
    Why do we have to multiply all the terms when we take the "In" out?
  2. jcsd
  3. Oct 14, 2012 #2

    Simon Bridge

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    Homework Helper

    Because what you do to one side has to be done to the other and ##a^{(b+c)}=a^ba^c## ... step by step:

    starting from:
    ##\ln|y|=x+\ln(x^2)+c## ... take the exponential of both sides:

    ##y=e^{x+\ln(x^2)+c}=e^x e^{\ln(x^2)}e^c##
  4. Oct 14, 2012 #3


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    The symbol is not "In" it is "ln" for logarithm.
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