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Second order differential equation

  1. Feb 10, 2015 #1
    1. The problem statement, all variables and given/known data
    So I'm in pchem right now and I haven't taken dif eq (it's not required, but I wish I had taken it now!)

    I am asked to solve this differential equation:

    y''+y'-2y=0

    2. Relevant equations

    I know for a second order differential equation I can solve for the roots first. If there is one root then the solution will take the form y=c1erx+c2xerx

    If there are two distinct roots I will get something like:
    y=c1er1x+c2er2x

    3. The attempt at a solution

    I tried to find the roots

    r2+r-2=0
    r= -2 and r=1

    So I get:

    y=c1e-2x+c2ex

    I am pretty sure this is correct (I checked to see if I got zero if I did y''+y'-2y and I did), but is there a way to find c1 and c2?
     
  2. jcsd
  3. Feb 10, 2015 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Not unless you have some initial values to work with, such as y(0) = 0 and y'(0) = 0. You'll need two initial values to determine c1 and c2.
     
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