1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Differential equation with Laplace transform

  1. Feb 3, 2010 #1
    1. The problem statement, all variables and given/known data
    [tex]t y'' + (3 t-1) y' + 3 y = 6 e^{-3t}[/tex]
    y(0) = 1
    y(5) = 2

    2. Relevant equations

    3. The attempt at a solution
    I tried applying the Laplace transform to the equation but I was having a little trouble...
    L [t·y''] = -dL[y'']/ds = s2·Y' + 2·s·Y - y(0) = s2·Y' + 2·s·Y - 1
    L [t·y'] = -dL[y']/ds = s·Y' + Y
    Therefore:
    [tex]s^2 Y' + 2 s Y - 1 + 3 s Y' +3 Y - s Y + 1+ 3 Y = \frac{6}{s+3}[/tex]
    [tex](s^2+3s)Y'+(s+6)Y=\frac{6}{s+3}[/tex]

    And then solve the Y(s) and then use the inverse transform.
    But it doesn't yield the correct result. I did the rest on the computer so I guess it's when I apply the transform where I make a mistake.

    Thanks for your help.
     
  2. jcsd
  3. Feb 3, 2010 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    I think you dropped the negative sign when calculating L[t y''] and L[t y'].
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...