1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Need explanation of this differential equation

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

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

    Answer:
    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    The symbol is not "In" it is "ln" for logarithm.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Need explanation of this differential equation
Loading...