# Math Help - Differential Equations

1. ## Differential Equations

if i have the general solution of a Differential Equation as:
\begin{equation*}
\bold{x}(t) = \left[ \begin {array}{c} u\\\noalign{\medskip}v\\\noalign{\medskip}w
\end {array} \right] = c_1\left[ \begin {array}{c} 1\\\noalign{\medskip}2\\\noalign{\medskip}1
\end {array} \right] e^{t} + (c_2 + c_3t)\left[ \begin {array}{c} -1\\\noalign{\medskip}0\\\noalign{\medskip}1
\end {array} \right] e^{-t} + c_3\left[ \begin {array}{c} -1\\\noalign{\medskip}1\\\noalign{\medskip}0
\end {array} \right] e^{-t}
\end{equation*}

.. if u have latex plug it in there ... frigg i cant get the code to work
How can i prove this formula includes all possible solutions.. Im pretty sure its using the Wronskian test but im not sure how to do for this! Any help?!

2. Edit it and use [ math ] and [ /math ] not "begin{equation*}" and "end{equation*}".

3. I found a site that explains the wronskian determinant for vectors, thanks i think i figured out the matrix thing.