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## Homework Statement

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

## Homework Equations

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

## 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?