1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Reduction of Order

  1. Aug 19, 2010 #1
    1. The problem statement, all variables and given/known data

    solve y"-4y'+4y=0 y1=e^(2x) using reduction of order

    3. The attempt at a solution

    I then substitute that into the original equation to get


    simplify to get

    from here I do not know what to do...I do know the answer is suppose to be xe^2x, but I don't know how that is done.
  2. jcsd
  3. Aug 19, 2010 #2


    User Avatar
    Homework Helper

    From u"e2x=0, you can divide by e2x and solve u''=0.
  4. Aug 19, 2010 #3
    ahh...so then u"=0 makes u'=c and then later u=xc1+c2 and

    but what then? how do I solve for c1 and c2?
  5. Aug 19, 2010 #4


    Staff: Mentor

    You need initial conditions in order to solve for the constants c1 and c2.
  6. Aug 19, 2010 #5
    however, in my solutions manual it says the solution comes out to be xe^2x, and I have no idea how that came to be. except for the use of this equation
    y2=y1S e^(-SP(x)dx)/y1^2 dx
  7. Aug 19, 2010 #6


    Staff: Mentor

    The general solution of your diff. equation is y = c1e^(2x) + c2xe^(2), for any values of c1 and c2. The simplest pair of linearly independent solutions is the pair with c1 = c2 = 1, so maybe they just arbitrarily chose that one.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook