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

Solve the following inital value problem

y_{1}' = y_{2}

y_{2}' = -5y_{1}-4y_{2}

with inital conditions y_{1}(0) = 1, y_{2}(0) = 0

2. Relevant equations

(A-[itex]\lambda[/itex]I)x = 0

3. The attempt at a solution

So I first started by setting out like this

y_{2}' = -5y_{1}- 4y_{2}

which then suggest 0 = -[itex]\lambda[/itex](-4-[itex]\lambda[/itex]) + 5

0 = [itex]\lambda[/itex]^{2}+4[itex]\lambda[/itex] + 5

But this is going to give me complex roots.. so I was just wondering have I made a mistake in my characteristic equation?

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

2. Relevant equations

3. The attempt at a solution

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

2. Relevant equations

3. The attempt at a solution

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# Solve the following intial value problem

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