Results 1 to 2 of 2

Math Help - Nonhomogeneous Equations and Undetermined Coefficients

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    124

    Nonhomogeneous Equations and Undetermined Coefficients

    y^(4) - 5y'' + 4y = e^x - xe^2x

    Find the general solution yp of the given equation
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    Solve the homogeneous equation

    your soln's are e^2x, e^(-2x) , e^x and e^(-x )
    for yp for the e^x term you'd normally have an Ae^x term but it is a homog solution so use Ax*e^x

    For x^e(2x) normally you would have a Bxe^(2x) and a Ce^(2x)

    but since e^(2x) is a solution to the homogeneous eqn

    multiply each by x so you'll have Bx^2e^(2x) and Cxe^(2x)

    yp = Axe^x + Bx^2*e^(2x) + Cx*e^(2x)

    Now you're ready to go to work
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Higher order differential equations, undetermined coefficients?
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: October 13th 2011, 04:06 PM
  2. [SOLVED] Second-Order Linear Nonhomogeneous DE with Constant Coefficients
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: April 26th 2011, 11:13 AM
  3. Method of undetermined coefficients - Nonhomogeneous Linear Systems
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: March 23rd 2009, 06:48 PM
  4. Differential equations - undetermined coefficients
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 12th 2009, 10:21 AM
  5. Undetermined Coefficients
    Posted in the Calculus Forum
    Replies: 5
    Last Post: July 5th 2007, 09:23 AM

Search Tags


/mathhelpforum @mathhelpforum