Results 1 to 5 of 5

Math Help - write the general solution to the differential equation

  1. #1
    Senior Member
    Joined
    Aug 2009
    Posts
    349

    write the general solution to the differential equation

    D^2(D^2+16)y=0

    ok so this is y=xC1 + C2sin 4x + C3cos 4x

    is this right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,553
    Thanks
    1423
    I assume this is supposed to mean

    \displaystyle \frac{d^4y}{dx^2} + 16\frac{d^2y}{dx^2} = 0.

    If you make the substitution \displaystyle Y = \frac{d^2y}{dx^2}, then this DE becomes

    \displaystyle \frac{d^2Y}{dx^2} + 16Y = 0,

    a second order linear constant coefficient homogeneous ordinary differential equation.

    I'm sure you can solve for \displaystyle Y = \frac{d^2y}{dx^2}, and use this to solve for \displaystyle y.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Aug 2009
    Posts
    349
    here is a problem i did earlier and got the answer right maybe this example can show what im trying to do...

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Aug 2009
    Posts
    349
    sorry here is the correction..

    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,696
    Thanks
    1467
    Quote Originally Posted by slapmaxwell1 View Post
    sorry here is the correction..

    Yes, that is correct. The characteristic equation can be written D(D+2)(D- 6)= 0 wo D= 0, -2, and 6 are characteristic roots.

    For your first problem, that's a fourth order equation and must have 4 indpendent solutions. The characteristic equation was D^2(D^2+ 16)= 0 which has D= 0 as a double root and D= 4i and D= -4i as the other roots. Because of the double root, you need both Ae^{0x}= A and Bxe^{0x}= Bx. The general solution to the equation is y(x)= A+ Bx+ Ccos(4x)+ Dsin(4x).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. general solution of this differential equation?
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: September 10th 2010, 07:57 AM
  2. General Solution of a Differential Equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 17th 2010, 02:39 AM
  3. general solution of a differential equation
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: December 5th 2009, 07:30 AM
  4. General solution to differential equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: November 13th 2009, 03:32 PM
  5. General Solution to Differential Equation
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: June 1st 2009, 12:12 PM

Search Tags


/mathhelpforum @mathhelpforum