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Homework Help: Differential equations - 2nd order homogenous eq'n w/ unknown

  1. Mar 23, 2007 #1
    Given that the equation
    t d^2y/dt^2 - (1+3t) dy/dt + 3y = 0. has a solution of the form e^ct, for some constant c, find the general solution (The answer is y(t) = c1(1+3t) + c2e^(3t)

    Edit: I finished this question as i figured it out. but when i come down to the last step, i get this
    y1(t) = e^3t
    y2(t) = -1/3t - 1/9

    y(t) = c1y1(t) + c2y2(t)
    y(t) = c1e^3t + c2(-1/3t-1/9)
    y(t) = c1e^3t + -1/9c2(3t+1)

    can i bet c3 = -1/9c2???
    so it's
    y(t) = c1e^3t + c3(3t+1)
    Last edited: Mar 23, 2007
  2. jcsd
  3. Mar 23, 2007 #2


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    Homework Helper
    Gold Member

    Why divide by t?

    Are you familiar with how the reduction of order method woks? This site should help
    http://tutorial.math.lamar.edu/AllBrowsers/3401/ReductionofOrder.asp [Broken]
    Last edited by a moderator: May 2, 2017
  4. Mar 23, 2007 #3
    sorry i figured out how to do it,
    can u confirm whether i am allowed to do the last step? i don't see why not but just incase
  5. Mar 23, 2007 #4


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    Gold Member

    Yes, it's right.
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