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How to solve the given differential equation

  1. Nov 17, 2006 #1
    Can someone give me some help, or at least tell me if I'm on the right track with this?

    Heres what I was given:
    4y'' - 4y' - 3y=0
    y(0)=1
    y'(0)=5

    Heres what I did:
    (sorry about the c1 and c2, I don't know how to make them show up as subsript)

    4(r^2) - 4r - 3 = 0
    r = 3/2 r=-1/2

    y = c1e^(3x/2) + c2e^(-x/2)

    1 = c1 + c2

    y'' = [3c1e^(3x/2)]/2 - [c2e^(-x/2)]/2

    5 = 3c1/2 - c2/2

    c2 = ±2sqrt(7) - 5

    c1 = 1/(±2sqrt(7) - 5) = [±2sqrt(7)]/3 + 5/3

    y = [(±2sqrt(7))/3 + 5/3]e(3x/2) + [±2sqrt(7) - 5]e(-x/2)

    Does this seem at all right?
     
  2. jcsd
  3. Nov 17, 2006 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Looks good to me!
     
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