(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If y_{3}(0) = 2y_{2}(0) - y_{1}(0), what is W(3)?

2. Relevant equations

[itex]\frac{d}{dt}[/itex] y(t) = A(t) y(t),

A(t) =

[1 e^{t}e^{-t}]

[e^{-t}0 e^{t}]

[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 y_{3}(t)=e^{At}*y_{3}(0)?

y_{3}(t)=e^{At}*(2y_{2}(0) - y_{1}(0))

where At =

[t te^{t}te^{-t}]

[te^{-t}0 te^{t}]

[2t tsin(t) -t]

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

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