Results 1 to 2 of 2

Math Help - Solving differential equations

  1. #1
    Newbie
    Joined
    Jun 2014
    From
    South Africa
    Posts
    1

    Question Solving differential equations

    Hi


    I am not very advanced in calculas.


    I need to solve for X(t)/Y(t) when t -> infinity.


    X'(t)+aX(t)+cX(t)-bY(t)=0 ....1 X(0)=0
    Y'(t)+bY(t)+cX(t)=0 .....2 Y(0)=0


    So I thought of deriving both equations to get:


    X''(t)+aX'(t)+cX'(t)-bY'(t)=0 ...3
    Y''(t)+bY'(t)+cX'(t)=0 ...4


    Then substituting 2 into 3 & substituting 1 into 4


    X''(t)+aX'(t)+cX'(t)-b*[bY(t)]-bcX(t)=0 ....5 Y''(t)+bY'(t)+cX(t)[a+c]+bY(t)=0 .....6


    Then substituting 1 into 5 Then substituting 2 into 6


    X''(t)+aX'(t)+cX'(t)+bX'(t)+baX(t)=0 Y''(t)+[a+b+c]Y'(t)+[ab+cb+b]Y(t)=0


    Taking the Laplace transform Taking the Laplace transform


    X(s)[s^2+s+a+c+sa+sc+sb+ba]=0 Y(s)[s^2+sa+2sb+sc+sab+scb-s-b]


    Then


    X(s)/Y(s)=[s^2+sa+2sb+sc+sab+scb-s-b]/[s^2+s+a+c+sa+sc+sb+ba]


    This is where I get stuck as I don't know how to transform it back to get X(t)/Y(t)


    Any help would be much appreciated.


    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    May 2014
    From
    Dallas, Texas
    Posts
    17
    Thanks
    5

    Re: Solving differential equations

    Quote Originally Posted by Mildred View Post
    Hi


    I am not very advanced in calculas.


    I need to solve for $\frac{x(t)}{y(t)}$ when $t \rightarrow\infty$


    $
    \begin{cases}
    x'(t)+ax(t)+cx(t)-by(t)=0\\
    y'(t)+by(t)+cx(t)=0
    \end{cases}$

    Given $x(0)=0$ and $y(0)=0$

    So I thought of deriving both equations to get:


    $\begin{cases}
    x''(t)+ax'(t)+cx'(t)-by'(t)=0\\
    y''(t)+by'(t)+cx'(t)=0
    \end{cases}$
    It would seem ill advised to me to make this a second order system considering you're only given two initial conditions(ICs). Basically anytime you have a DE when you solve them you're always doing some type of integration in order to solve them and in order to fully solve a DE you need the same number of initial conditions as the highest order derivative in the DE. In this case you are give 2 first order equations with 2 initial conditions so the system is solvable; however, in your first step you turn the system into a second order system of 2 equations so now you would need 4 initial conditions in order to solve it. Since you're not given 4 ICs you should keep this a first order system.

    You're on the right track as far as taking the Laplace Transform of both equations. Take the Laplace Transform of the above system and solve it for $x(t)$ and $y(t)$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving differential equations...
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 6th 2014, 11:07 AM
  2. Solving Differential Equations
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 3rd 2010, 09:18 AM
  3. Solving three differential equations
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: August 28th 2009, 11:31 AM
  4. Solving differential equations
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 10th 2008, 10:36 AM
  5. Help on solving differential equations...
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: October 19th 2008, 03:14 PM

Search Tags


/mathhelpforum @mathhelpforum