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Homework Help: Laplace transorm problem

  1. May 3, 2012 #1
    1. The problem statement, all variables and given/known data
    Using the laplace transform technique, solve the ordinary differential equation:
    d2y/dt2+4.2dy/dt+4.5y=0 initial conditions: y(0)=1 and y'(0)=1

    2. Relevant equations
    From laplace tables:

    3. The attempt at a solution
    After using the laplace tables to convert the equation, and rearranging it to make Y the subject, I have come to this point:
    Iv tried completing the square on the denominator and other methods but cannot get to a point that looks similar to the laplace tables in order to convert it back. Im pretty sure i need to use the ones under the section "General approach to quadratic functions of the form as2 + bs + c" however i have completely no idea as to what to do with α and β
  2. jcsd
  3. May 3, 2012 #2
  4. May 4, 2012 #3
    Thamkyou for the link, however you cannot factorise the denominator, unless you complete the square. Can you use the partial fraction method with completing the square?
  5. May 4, 2012 #4
    Your denominator can certainly complete the square, s^2+4.2s+4.5=(s+2.1)^2-2.1^2+4.5, doesn't it? Obviously no need for partial fraction decomposition :biggrin:
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