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: 2nd Order Linear Diff. Eqn (homogeneous)

  1. May 5, 2008 #1

    aznkid310

    User Avatar

    1. The problem statement, all variables and given/known data
    Show that id y = x(t) is a solution of the diff. eqn. y'' + p(t)y' + q(t)y = g(t), where g(t) is not always zero, then y = c*x(t), where c is any constant other than 1, is not a solution.


    2. Relevant equations
    Can someone help me get started?
    Also, since g(t) is not zero, this means that the equation is nonhomogeneous?


    3. The attempt at a solution
     
    aznkid310, May 5, 2008
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. May 6, 2008 #2

    Defennder

    User Avatar
    Homework Helper

    Yes, this implies the DE is non-homogenous. To show that y = c*x(t) is not a solution just substitute that into the DE. Do you still get g(t) on the RHS?
     
    Defennder, May 6, 2008
  4. May 6, 2008 #3

    aznkid310

    User Avatar

    For y = c*x(t): x''(t) + p(t)*x'(t) + q(t)*x(t) = g(t)

    What next?
     
    aznkid310, May 6, 2008
  5. May 6, 2008 #4

    Defennder

    User Avatar
    Homework Helper

    Note that it is given that y=x(t) is a solution, that means x''(t) + p(t)x'(t) + q(t)x(t) = g(t). The expression you get when you substitute y = cx(t) into the DE is clearly different from this. What does that tell you?
     
    Defennder, May 6, 2008
  6. May 6, 2008 #5

    HallsofIvy

    User Avatar
    Science Advisor

    What happened to the c?? If x''(t) + p(t)*x'(t) + q(t)*x(t) = g(t) what is
    (c*x)'' + p(t)*(c*x)' + q(t)*(c*x)?
     
    HallsofIvy, May 6, 2008
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook