Results 1 to 8 of 8

Math Help - [SOLVED] need help on homogeneous ODE

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    60

    [SOLVED] need help on homogeneous ODE

    Hi can someone help me on this eqn..Btw im new here..cheers

    y''''-4y'''+7y''-6y'+2y=0

    It is to find the general solution..
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
    Posts
    397
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ashes View Post
    Hi can someone help me on this eqn..Btw im new here..cheers

    y''''-4y'''+7y''-6y'+2y=0

    It is to find the general solution..
    This is a linear constant coefficient homogeneous ODE, so:

    First solve the charateristic equation:

    \lambda^4-4 \lambda^3+7\lambda^2-6\lambda+2=0

    The roots of this are \lambda=1 (with multiplicity 2) and \lambda=1 \pm i , and your notes should tell you where to go from here.

    RonL
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Mar 2008
    Posts
    60
    therefore the r=1(with multiplicity 2) is actually a double root not a distinct root right?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ashes View Post
    therefore the r=1(with multiplicity 2) is actually a double root not a distinct root right?

    yes

    RonL
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Mar 2008
    Posts
    60

    differential eq

    some help on solving this homogeneous ODE pls..

    y''''+4k^4y=0 where k is non zero constant
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ashes View Post
    some help on solving this homogeneous ODE pls..

    y''''+4k^4y=0 where k is non zero constant
    Here the charateristic equation is:

    \lambda^4+4k^4=0

    or:

    \lambda^4=-4k^4=4k^4 e^{\pi i+2n\pi i}\ n=0,\ \pm 1,\ \pm2, ..

    so:

    \lambda = |k|\sqrt{2}~e^{\pi i/4+n\pi i/2},\ n=0, \ \pm 1,\ \pm2, ...

    and you will get four distinct values for \lambda for n=0, \ 1,\ 2,\ 3

    and the rest follows.

    RonL
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by ashes View Post
    some help on solving this homogeneous ODE pls..

    y''''+4k^4y=0 where k is non zero constant
    In future post new questions into new threads, that way we can see that
    they need attention, and will probably be answered sooner.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Homogeneous system
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 1st 2010, 04:46 PM
  2. [SOLVED] First order non linear non homogeneous DE
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 3rd 2010, 12:19 PM
  3. [SOLVED] First order homogeneous ODE
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: August 19th 2009, 12:06 PM
  4. [SOLVED] 1st order homogeneous diffeq from G.F.Simmons
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: August 17th 2009, 02:50 PM
  5. [SOLVED] homogeneous DEQ
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 29th 2007, 07:23 AM

Search Tags


/mathhelpforum @mathhelpforum