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Help putting differential equations into matrix form

  1. Nov 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Hello, I am trying to put the following equations in to matrix form in order to solve the system. If anyone could please explain to me how to do it or show me an example it would be awesome.

    All material given in question:

    For the system of inhomogeneous differential equations,
    dx/dt = 5x-y+2

    dy/dt = x + 3y – 4t

    and the initial condition, x(0)=1 and y(0)=2.

    a)Arrange the system into matrix form
    b)Find the diagonal or Jordan form of the system matrix
    c)Write the general solution in the form of the matrix exponential
    d)Use the initial condition to find the solution x(t) and y(t)

    Thanks for any help

    2. Relevant equations



    3. The attempt at a solution

    I am aware that the matrix has to be square in order to proceed.

    What i have so far is:

    [5 -1 0 ] [x] + [2]
    [1 3 -4 ] [y] + [0]
    [0 0 0 ] [t] + [0]

    The -4t is what is throwing me off because there is no dt/dt equation given so i have put all 0's in the matrix.
     
  2. jcsd
  3. Nov 18, 2013 #2

    LCKurtz

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    ##t## is your independent variable. Write your system in the form$$
    \begin{bmatrix} x'\\y'
    \end{bmatrix}=
    \begin{bmatrix}
    a&b\\c&d
    \end{bmatrix}
    \begin{bmatrix}
    x\\y
    \end{bmatrix}+
    \begin{bmatrix}
    f(t)\\g(t)
    \end{bmatrix}$$
     
  4. Nov 18, 2013 #3
    So would the matrix form be:

    5 -1 , x + 2
    1 3 ,y + -4t

    thanks for the help
     
  5. Nov 18, 2013 #4

    LCKurtz

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    I showed you one form. But yours isn't like mine because you have no derivatives nor equals signs. Surely your text shows you what form to use.
     
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