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## Homework Statement

Find the general solution of the equation

u'' + u' + 2u = 0 of the form u(t) = C*(e^a*t)* cos[B*t +Q],

1)Verify that it satisfies u(t+2pi/sqrt[7])=-e^(-pi/sqrt[7])*u(t)

2)Consider a solution satisfying u(0) = 1. Determine u(2pi/sqrt[7])

For what other values of t can you determine u(t) given u(0)?

## Homework Equations

## The Attempt at a Solution

p^2+p+2=0

delta=-1

p1=-1/2+(i*sqrt[7])/2 and p2=-1/2-(i*sqrt[7])/2

=>C*(e^-1/2*t)* cos[(sqrt[7]/2)*t +Q]=>(e^(-t/2)-(pi/sqrt[7]))*C*cos[(sqrt[7]/2)*t +pi+Q],pi+Q=a constant=>-e^(-pi/sqrt[7])*u(t).I hope this is ok.

I also need help with 2)