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October 16th, 2015, 04:53 PM   #1
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matrix-vector representation for a system of ODE's

I am aiming to explicitly write the matrix-vector representation of this system.
y’1 = 5y2 - y1 + y3;
y’2 = 3y1 - y2 + t2;
y’3 = y3 - ty2

This is what I have so far:
[ y’1 ] [ -1 5 1] [ 0]
[ y’2 ] = [ 3 -1 0] [ t2]
[ y’3 ] [ 0 ? 1] [ ? ]
Just not sure how to attack -ty2
Any help would be appreciated, thanks guys
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October 17th, 2015, 11:59 AM   #2
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"t2" is $\displaystyle t^2$, right? (Since you are using "y1", "y2", and "y3" as subscripts, it would be better to write t^2 for "t squared".)

"-t y2" is -t times y2 so that would be
$\displaystyle \begin{bmatrix} y_1 \\ y_2 \\ y_3\end{bmatrix}= \begin{bmatrix}-1 & 5 & 1 \\ 3 & -1 & 0 \\ 0 & -t & 2\end{bmatrix}\begin{bmatrix} y_1 \\ y_ 2 \\ y_3\end{bmatrix}+ \begin{bmatrix}0 \\ t^2 \\ 0 \end{bmatrix}$.
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