1. Not finding help here? Sign up for a free 30min 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!

Explicit check for Laplace transform?

  1. Jan 14, 2016 #1
    1. The problem statement, all variables and given/known data
    Solve the following initial value problem using Laplace transforms: y' + 4y = 3t3 e−4t ; y(0) = 0 . Useful information: Recall that the Laplace transform of y 0 is pY − y(0), where Y is the Laplace Transform of y. The Laplace transform of tk e−at is k!/(p + a)k+1 . Confirm the validity of your result by an explicit check.

    2. Relevant equations
    tk e−at is k!/(p + a)k+1

    3. The attempt at a solution
    So I have the solution:

    y=3/4 t4e−4t

    And I know this is correct.

    However is there a specific check I can do to make sure this is correct? ie. What is the explicit check?
     
  2. jcsd
  3. Jan 14, 2016 #2

    Samy_A

    User Avatar
    Science Advisor
    Homework Helper

    If you understand what a differential equation is, the specific check you could do becomes self-evident.

    Said differently: you claim to have the solution. What does it mean that y=3/4 t4e−4t is the solution?
     
  4. Jan 14, 2016 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Suppose somebody gave you the alleged solution ##y = (3/4) t^4 e^{-4t}## but did not tell you where it came from; how could you check if it is correct?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Explicit check for Laplace transform?
  1. Laplace transformation (Replies: 2)

  2. Laplace transform (Replies: 3)

  3. Laplace Transforms (Replies: 41)

Loading...