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DE with initial conditions with repeated rootsplease check work thanks

  1. Feb 19, 2012 #1
    1. The problem statement, all variables and given/known data
    4y'' - 4y' + y = 0
    y(1) = -4
    y'(1) = 0


    2. Relevant equations

    getting the coeff's gets messier and messier.. am i doing something wrong?

    3. The attempt at a solution

    4y'' - 4y' + y = 0
    y'' - y' - (1/4)y = 0

    r_1 = r_2 = 1/2

    general soln:
    y(t) = c_1e^(t/2) + c_2te^(t/2)
    y'(t) = (1/2)c_1e^(t/2) + [(e^(t/2) + (1/2)te^(t/2)]c_2

    now applying init cond...

    -4 = c_1e^(1/2) + c_2e^(1/2)
    0 = (1/2)c_1e^(1/2) + [(e^(1/2) + (1/2)e^(1/2)]c_2

    after trying to solve for c_2 I am ending up with c_1 = -4/e^(1/2) - (4/3)/e
    but i stopped here because it looks completely wrong... please help any help is really appreciated ...thanks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 19, 2012 #2
    Should be y'' - y' + (1/4)y = 0.
     
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