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!

Re-write as a system of first order ODEs

  1. May 30, 2012 #1
    hello,

    I am going through the first chapter (a review chapter) of a second-course book in ODEs, and can't seem to remember how to re-write higher order DEs into a system of first order linear ODEs, and my old textbook only shows this for second order equations...

    The question is: "Write the following differential equations as a system of first order ODEs:

    y'' -5y'+6y=0
    -y''-2y' = 7cos(y')
    y(4) - y'' + 8y' + y2 = ex "
     
  2. jcsd
  3. May 30, 2012 #2
    How about letting [itex]y=y_0, y'=y_1[/itex] et cetera?
     
  4. May 30, 2012 #3
    You have to make a change of variable, you can call y'=z and by doing the substitution you obtain a first order system of ODE.

    Sorry for my English and I'll do it later from my computer if I haven't explained myself properly.
     
  5. May 30, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Add the first two equations to eliminate y'' .

    Is the really cos(y') and not cos(y) ?

    Getting rid of the 4th derivative may be more difficult. I think you can differentiate the first two, one of them once, the other twice to eliminate y(4) (and the y''' you'll introduce).

    Alternatively: If that's a cos(y), then you could combin the first two equations to eliminate y'. Differentiate that twice to get an additional equation with y(4) and y' and y. Combine that with the third equation to eliminate y(4) .
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook