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 October 16th, 2015, 04:53 PM #1 Newbie   Joined: Oct 2015 From: Australia Posts: 1 Thanks: 0 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
 October 17th, 2015, 11:59 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 "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 $\displaystyle \begin{bmatrix} y_1 \\ y_2 \\ y_3\end{bmatrix}= \begin{bmatrix}-1 & 5 & 1 \\ 3 & -1 & 0 \\ 0 & -t & 2\end{bmatrix}\begin{bmatrix} y_1 \\ y_ 2 \\ y_3\end{bmatrix}+ \begin{bmatrix}0 \\ t^2 \\ 0 \end{bmatrix}$.

 Tags matrixvector, ode, representation, system

y 0 1 = 5y2 − y 1 y 3 y 0 2 = 3y1 − y2 t 2 y 0 3 = y3 − ty2

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