# Homework Help: Systems of first order linear equations involving wronskian and matrices

1. Nov 27, 2011

### bbb3

1. The problem statement, all variables and given/known data

If y3(0) = 2y2(0) - y1(0), what is W(3)?

2. Relevant equations

$\frac{d}{dt}$ y(t) = A(t) y(t),

A(t) =
[1 et e-t]
[e-t 0 et]
[2 sin(t) -1]

3. The attempt at a solution

I already solved the Wronskian W(t)=c*e∫(1+0-1)dt=c

What I was not sure about was how to go about solving for the general solution of the y's.

Would it be y3(t)=eAt*y3(0)?

y3(t)=eAt*(2y2(0) - y1(0))
where At =
[t tet te-t]
[te-t 0 tet]
[2t tsin(t) -t]