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!

Need help with finding particular solution to a second order differential equation

  1. Nov 10, 2009 #1
    1. The problem statement, all variables and given/known data
    Consider the differential equation:
    y''+10y'+25y= f(x)

    Find a particular solution if f(x) = 32xe^(-x)

    2. Relevant equations
    I already did the general solution when f(x)=0 and that is Ae^(-5x) + Bxe^(-5x)


    3. The attempt at a solution
    I tried yp=axe^(-x) and got a= 4x+2 which is wrong

    The answer is (2x-1)e^(-x)

    does anyone know what particular solution i can try in order to get the answer?

    Thanks
     
  2. jcsd
  3. Nov 10, 2009 #2

    Mark44

    Staff: Mentor

    Re: Need help with finding particular solution to a second order differential equatio

    If f(x) had been 32e-x, you would want to try yp = Ae-x. Since f(x) = 32xe-x, you want your particular solution to be yp = Ae-x + Bxe-x.

    If f(x) had been 32x2e-x, you would try a particular solution of the form yp = Ae-x + Bxe-x + Cx2e-x. There's a reason for all of this, but I'll leave that for your instructor.

    BTW, this is hardly a Precalculus question. You should have posted it in Calculus and Beyond.
     
  4. Nov 10, 2009 #3
    Re: Need help with finding particular solution to a second order differential equatio

    Hi, thankyou so much for your reply. I tried it and it worked!!! i shall write it down and remember that forever now!

    Also, sorry about posting in the wrong section! I can't believe i did that because i took so long to check that my post was right.. i guess i forgot to check if i had clicked on the right section..! Thankyou so much though.
     
  5. Nov 10, 2009 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Need help with finding particular solution to a second order differential equatio

    Generally speaking when a "right hand side" involves an [itex]n^{th}[/itex] power of x, you should try a polynomial of degree n down.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Need help with finding particular solution to a second order differential equation
Loading...