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ODE Theory Question

  1. Feb 7, 2013 #1
    1. The problem statement, all variables and given/known data

    We have y'' + 4y' + 4y = 0 ; find the general solution.

    2. Relevant equations

    Reduction of Order.

    3. The attempt at a solution

    So when determining the roots of the characteristic equation, -2 was a double root, and therefore we can't simply have c1e-2t + c2e-2t. So I thought I would use reduction of order to get a second equation. However in the solution, they just left it c1e-2t + c2e-2t and I'm wondering if what I was taught to do in the case of non distinct roots was wrong, or if the solution is wrong.
    Last edited: Feb 7, 2013
  2. jcsd
  3. Feb 7, 2013 #2


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    The solution appears to be wrong.

    y = c1*exp(-2t) + c2 * t * exp(-2t)
  4. Feb 7, 2013 #3


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    Please show exactly what you did in your attempted reduction of order. When I try a solution of the form [itex]y= u(t)e^{-2t}[/itex], I get [itex]u(t)= A+ Bt[/itex] giving [itex]y= Ae^{-2t}+ Bte^{-2t}[/itex] as general solution.
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