Help putting differential equations into matrix form

[hajjar0415]

Homework Statement

Hello, I am trying to put the following equations into 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

Homework Equations

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.

 

[LCKurtz]

$t$ is your independent variable. Write your system in the form$$
\begin{bmatrix} x'\\y'
\end{bmatrix}=
\begin{bmatrix}
a&b\\c&d
\end{bmatrix}
\begin{bmatrix}
x\\y
\end{bmatrix}+
\begin{bmatrix}
f(t)\\g(t)
\end{bmatrix}$$

 

[hajjar0415]

So would the matrix form be:

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

thanks for the help

 

[LCKurtz]

So would the matrix form be:

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

thanks for the help

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.