# System of differential equations, Maple tells me I'm wrong

1. Sep 10, 2010

### Nihuepana

Hi there,

I have a system of differential equations which I set up in a matrix like this:

\left[ \begin {array}{ccc} 3/2&-1&-1/2\\ \noalign{\medskip}-1/2&2&1/2 \\ \noalign{\medskip}1/2&1&5/2\end {array} \right] = \left[ \begin {array}{c} {\frac {d}{dt}}x \left( t \right) \\ \noalign{\medskip}{\frac {d}{dt}}y \left( t \right) \\ \noalign{\medskip}{\frac {d}{dt}}z \left( t \right) \end {array} \right]

Now I need to find the real solution to the system, so I find the eigenvectors and eigenvalues
Eigenvalues <3,1,2> and Eigenvectors <-1,1,1>,<-1,-1,1> and <1,-1,1>

and set up my solution like this

cn*elambdan*t*vn

I even get a nice matrix out saying
\left[ \begin {array}{c} {\frac {d}{dt}}x \left( t \right) \\ \noalign{\medskip}{\frac {d}{dt}}y \left( t \right) \\ \noalign{\medskip}{\frac {d}{dt}}z \left( t \right) \end {array} \right] = \left[ \begin {array}{c} -{\it c\_2}\,{{\rm e}^{3\,t}}-{ \it c\_3}\,{{\rm e}^{t}}+{\it c\_1}\,{{\rm e}^{2\,t}} \\ \noalign{\medskip}{\it c\_2}\,{{\rm e}^{3\,t}}-{\it c\_3}\,{{\rm e} ^{t}}-{\it c\_1}\,{{\rm e}^{2\,t}}\\ \noalign{\medskip}{\it c\_2}\,{ {\rm e}^{3\,t}}+{\it c\_3}\,{{\rm e}^{t}}+{\it c\_1}\,{{\rm e}^{2\,t}} \end {array} \right]

But Maple keeps giving me this solution instead:

$$\left\{ x \left( t \right) ={\it \_C1}\,{{\rm e}^{2\,t}}+{\it \_C2}\, {{\rm e}^{3\,t}}+{\it \_C3}\,{{\rm e}^{t}},y \left( t \right) =-{\it \_C1}\,{{\rm e}^{2\,t}}-{\it \_C2}\,{{\rm e}^{3\,t}}+{\it \_C3}\,{ {\rm e}^{t}},z \left( t \right) ={\it \_C1}\,{{\rm e}^{2\,t}}-{\it \_C2}\,{{\rm e}^{3\,t}}-{\it \_C3}\,{{\rm e}^{t}} \right\}$$

I really can't figure out the problem here - is there something wrong with my eigenvectors or is it the solution I'm doing all wrong? Hope you can help :)