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How to solve this problem using laplace transform?

  1. Nov 17, 2015 #1
    1. The problem statement, all variables and given/known data
    The differential equation given:
    y''-y'-2y=4t2

    2. Relevant equations


    3. The attempt at a solution
    I used the laplace transform table to construct this equation,and then I did partial fraction for finding the inverse laplace transform.But I'm now stuck at finding the inverse laplace transform of 1/s^3 and 1/s^2...

    And the attached photo is the attempted solution.
    View attachment 92000
     

    Attached Files:

  2. jcsd
  3. Nov 17, 2015 #2

    Mark44

    Staff: Mentor

    I didn't verify your work, but here is a table of Laplace transforms - http://web.stanford.edu/~boyd/ee102/laplace-table.pdf
     
  4. Nov 18, 2015 #3
  5. Nov 18, 2015 #4

    Mark44

    Staff: Mentor

    Look just below the one for 1/s2. It's a more general formula.
     
  6. Nov 18, 2015 #5

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    If you know the inverse transform of 1/s, then you can get the inverse transform of 1/s^2 by integration, and of 1/s^3 by integration again. Remember: there are some standard general transform results that are helpful. Below, let ## f(t) \leftrightarrow g(s) = {\cal L}(f)(s)##. Then:
    [tex] \begin{array}{l} \displaystyle \frac{df(t)}{dt} \leftrightarrow s g(s) - f(0+)\\
    \int_0^t f(\tau) \, d \tau \leftrightarrow \displaystyle \frac{1}{s} g(s)
    \end{array}
    [/tex]
    These were given specifically in the table suggested by Mark44; did you miss them?
     
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