Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Laplace transform for set of differential equations

  1. May 13, 2014 #1
    I have a set of differential equations with the basic form:

    dy_n/dt = t*(a_(n-1)*y_(n-1)+b(n+1)*y_(n+1)-2c_n*y_n)

    So the time depence is a simple factor in front of the coefficient matrix. Does this set of differential equations have closed form solutions?
     
    Last edited: May 13, 2014
  2. jcsd
  3. May 14, 2014 #2

    pasmith

    User Avatar
    Homework Helper

    Change the independent variable to [itex]x[/itex], where [tex]\frac{dy_n}{dt} = t\frac{dy_n}{dx}.[/tex] The resulting system is linear with constant coefficients and therefore has a closed form solution.
     
  4. May 14, 2014 #3
    Nice! So I should substitute x=½t2?
    Will this work for any system where the time dependence may be pulled outside the parenthesis on the RHS like in my example?
    Also if I get a system with constant coefficients I may obtain a steady state solution where dy_n/dx=0. That does not seem realistic considering i started off with a system with time dependent coefficients.
     
    Last edited: May 14, 2014
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Laplace transform for set of differential equations
Loading...