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For the following fuctions I'd like your help with finding Wronskian determinant: $y_2(t)=\begin{pmatrix} e^t\\ e^t \end{pmatrix}, y_1(t)=\begin{pmatrix} t^2\\ 2t \end{pmatrix}$.

Wornskian determinant defined by $\mathbb{W}(y_1,y_2)=\begin{vmatrix} y_1 & y_2 \\ y_1' & y_2' \end{vmatrix}$.

How should I solve find it with the given $y_1$ and $y_2$? What should I use?

Thanks a lot.

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    so it's just $t^$2$ e^t-$2$te^t$?2012-05-20

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The Wronskian for a system $\{y_i(t)=(y_{i1}(t),\ldots,y_{in}(t)\}_{i=1,\ldots,n}$ of solutions for a $n\times n$ system of first order linear edo is given by $\mathbb{W}[y_1,\ldots,y_n](t)=\det(y_{ij}(t))$.

So in your case it should be $\left|\begin{array}{cc}t^2&2t\\e^t&e^t\end{array}\right|=(t^2-2t)e^t.$

I hope it helps.