Results 1 to 4 of 4

Math Help - Coupled Differential Equations

  1. #1
    Newbie
    Joined
    Aug 2011
    Posts
    7

    Coupled Differential Equations

    Hey, I've been set a question which i have no idea how to attempt. Please could some one show me some guidance? thanks

    Question:

    y'(x) +z(x)= x
    z'(x) +4y(x)=0
    y(0)=1
    z(0)=-1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,315
    Thanks
    1225

    Re: Coupled Differential Equations

    Quote Originally Posted by Downes View Post
    Hey, I've been set a question which i have no idea how to attempt. Please could some one show me some guidance? thanks

    Question:

    y'(x) +z(x)= x
    z'(x) +4y(x)=0
    y(0)=1
    z(0)=-1
    What has the question asked you to do?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2011
    Posts
    7

    Re: Coupled Differential Equations

    It asks to solve it
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,315
    Thanks
    1225

    Re: Coupled Differential Equations

    Quote Originally Posted by Downes View Post
    Hey, I've been set a question which i have no idea how to attempt. Please could some one show me some guidance? thanks

    Question:

    y'(x) +z(x)= x
    z'(x) +4y(x)=0
    y(0)=1
    z(0)=-1
    From the first equation we have \displaystyle \frac{dy}{dx} + z = x \implies z = x - \frac{dy}{dx} \implies \frac{dz}{dx} = 1 - \frac{d^2y}{dx^2}.

    Substituting this into the second equation gives

    \displaystyle 1 - \frac{d^2y}{dx^2} + 4y = 0 \implies \frac{d^2y}{dx^2} - 4y = 1.

    This is a second order linear constant coefficient nonhomogeneous DE, which is easy to solve.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. coupled differential equation
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: May 24th 2010, 03:55 AM
  2. Replies: 4
    Last Post: April 23rd 2010, 07:11 AM
  3. Coupled differential equations
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: November 15th 2009, 06:50 AM
  4. coupled equations
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: November 9th 2009, 11:04 PM
  5. Coupled differential Equations
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 14th 2008, 05:44 AM

Search Tags


/mathhelpforum @mathhelpforum