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!

2nd ODE constant coeff, quick question

  1. Feb 17, 2008 #1

    rock.freak667

    User Avatar
    Homework Helper

    1. The problem statement, all variables and given/known data
    Solve:
    [tex]\frac{d^2y}{dx^2}+\frac{dy}{dx}=3x^2+2x+1[/tex]

    3. The attempt at a solution

    Well the C.F. is [itex]y=C_1e^{-x}[/itex]
    the P.I. is of the form [itex]y_{PI}=Ax^3+Bx^2+Cx+D[/itex]

    I can find the values of A,B and C bu differentiating it and substituting it into the equation. But How would I find D since there is no 'y' in the ODE given and differentiating [itex]y_{PI}[/itex] makes the constant disappear.



    (Note: I can find the answer by integrating it w.r.t x and then using the integrating factor but I would like to know how to find it by adding the PI and CF together)
     
  2. jcsd
  3. Feb 17, 2008 #2
    The D is redundant since one of the solutions to the natural equation is a constant function.

    Therefor the constant function is determined by the initial conditions rather then the forcing function.
     
  4. Feb 17, 2008 #3

    rock.freak667

    User Avatar
    Homework Helper

    Ah...thanks then,I thought I was really doing something wrong.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: 2nd ODE constant coeff, quick question
  1. Quick ODE question (Replies: 4)

  2. 2nd ODE (Replies: 2)

Loading...