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prehisto

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## Homework Statement

System1:

dx/dt=x+y

dy/dt=8x-y

## Homework Equations

## The Attempt at a Solution

detreminant=(1-λ)(-1-λ)=(λ-3)(λ+3);λ[itex]_{1}[/itex]=-3 and λ[itex]_{2}[/itex]=3

So system 2:

(1-λ)[itex]\alpha[/itex]+[itex]\beta[/itex]=0

8[itex]\alpha[/itex]+(-1-λ)[itex]\beta[/itex]=0

When i put λ[itex]_{1}[/itex]=-3 in system 2 -> [itex]\alpha[/itex] and [itex]\beta[/itex]=0.

the same goes for λ[itex]_{2}[/itex]

That menas that solution in form of y=C_1*[itex]\beta[/itex]_1*exp(λ[itex]_{1}[/itex]*t)+C_2*[itex]\beta[/itex]_2*exp(λ[itex]_{2}[/itex]*t) is equal to 0. Thats wrong.

Where is my mistake?

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