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!

How to deal with homogenous differential equation system?

  1. Nov 17, 2011 #1
    How to deal with homogenous differential equation system??

    1. The problem statement, all variables and given/known data

    s'[t] == (-3 s[t])/580, m'[t] == (-19 m[t])/590,
    h'[t] == (3 s[t])/580 + (19 m[t])/590 - (2 h[t])/25,
    e'[t] == (2 h[t])/25 - (85 e[t])/116,
    o'[t] == (85 e[t])/116 - (33 o[t])/131

    2. Relevant equations

    it is a system to clean the Great lake that five lakes linked together

    3. The attempt at a solution

    and I know that the solution for s and m are 2900*E^(-3 t/580) and 1180*E^(-19 t/590)
    as s[0]=2900, m[0]=1180. and h[0]=850, e[0]=116, o[0]=393

    I really want someone can tell me any math software can work with this or any way to do it
     
  2. jcsd
  3. Nov 18, 2011 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: How to deal with homogenous differential equation system??

    Okay, since you were able to solve for s and m, put those into the equation for h and it becomes pretty straight forward. Once you know h, you can put that into the equation for e and then put the solution for e into the equation for o.

    Or you can write it as the matrix equation
    [tex]\begin{pmatrix}s \\ m \\ h \\ e \\ 0\end{pmatrix}'= \begin{pmatrix}-\frac{3}{580} & 0 & 0 & 0 & 0 \\ 0 & -\frac{19}{580} & 0 & 0 & 0 \\ \frac{3}{580} & \frac{19}{580} & -\frac{2}{25} & 0 & 0 \\ 0 & 0 & \frac{2}{25} & -\frac{85}{116} & 0 \\ 0 & 0 & 0 & \frac{85}{116} & -\frac{33}{131}\end{pmatrix}\begin{pmatrix}s \\ m \\ h \\ e \\ 0\end{pmatrix}[/tex]
    Since that is a triangular matrix, its eigenvalues are just the numbers on the main diagonal.
     
  4. Nov 18, 2011 #3
    Re: How to deal with homogenous differential equation system??

    I know how to do with the X'=AX that x=c1e^λt[u1]....however, what I get is a single equation. I have no idea how to deal with five variables....
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook