Results 1 to 8 of 8

Math Help - solve the given differential by undetermined coefficients...

  1. #1
    Senior Member
    Joined
    Aug 2009
    Posts
    349

    solve the given differential by undetermined coefficients...

    ok so here is the problem

    y'' +3y = -48(x^2)(e^3x)

    ok so i get the first few couple of steps,

    m^2 +3 = 0, m = +/- sqrt(3)i

    so Yc = C1cos sqrt(3)x + C2sin sqrt(3)x

    Yp = (Ax^2 +Bx + C)e^3x

    so how do i find Yp? well let me ask first, is my setup right so far?

    i need a lil help on this one....
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Just plug Yp into the DE and equate like powers of x (the exponentials will cancel, I think). Where does that place you?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,589
    Thanks
    1445
    Quote Originally Posted by slapmaxwell1 View Post
    ok so here is the problem

    y'' +3y = -48(x^2)(e^3x)

    ok so i get the first few couple of steps,

    m^2 +3 = 0, m = +/- sqrt(3)i

    so Yc = C1cos sqrt(3)x + C2sin sqrt(3)x

    Yp = (Ax^2 +Bx + C)e^3x

    so how do i find Yp? well let me ask first, is my setup right so far?

    i need a lil help on this one....
    Your setup looks fine so far.

    Now since you know that \displaystyle y_p = (Ax^2 + Bx + C)e^{3x}, what are \displaystyle y'_p and \displaystyle y''_p?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Aug 2009
    Posts
    349
    ok so Yp'= (2Ax + B)e^(3x) + 3(Ax^2+ Bx + C)e^(3x) and Yp'' = well its gonna be long :O)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,589
    Thanks
    1445
    Yes, but you need to evaluate it. Because the next step is to substitute \displaystyle y''_p and \displaystyle y_p into your DE, then simplify so that you can equate the coefficients of the like powers of \displaystyle x.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Senior Member
    Joined
    Aug 2009
    Posts
    349
    Yp''= 2Ae^(3x) + 3(2Ax + B)e^(3x) + 3(2Ax+B)e^(3x)+9(Ax^2+Bx+C)e^(3x) <----is this right?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member
    Joined
    Aug 2009
    Posts
    349
    ok i will evaluate it...so i substitute in the Y' and Y'' and then solve for A B and C
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,589
    Thanks
    1445
    Is \displaystyle y' part of your DE?
    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, 03:06 PM
  2. solve the differential equation by undetermined coefficients
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 15th 2011, 11:41 AM
  3. Replies: 1
    Last Post: May 4th 2009, 07:21 PM
  4. Replies: 8
    Last Post: March 14th 2009, 06:29 PM
  5. Differential equations - undetermined coefficients
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 12th 2009, 09:21 AM

Search Tags


/mathhelpforum @mathhelpforum