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October 16th, 2015, 04:53 PM  #1 
Newbie Joined: Oct 2015 From: Australia Posts: 1 Thanks: 0  matrixvector representation for a system of ODE's
I am aiming to explicitly write the matrixvector 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 $\displaystyle \begin{bmatrix} y_1 \\ y_2 \\ y_3\end{bmatrix}= \begin{bmatrix}1 & 5 & 1 \\ 3 & 1 & 0 \\ 0 & t & 2\end{bmatrix}\begin{bmatrix} y_1 \\ y_ 2 \\ y_3\end{bmatrix}+ \begin{bmatrix}0 \\ t^2 \\ 0 \end{bmatrix}$. 

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