# Math Help - general solution of the equation

1. ## general solution of the equation

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. and 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)?

Now r^2+r+2=0=>delta=-1=>
r1=-1/2+(i*sqrt[7])/2 and r2=-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.
And with 2 I have no clue...

2. anyone...should i rewrite it again to be more inteligible?

3. Originally Posted by AkilMAI
anyone...should i rewrite it again to be more inteligible?
Re-writing in LaTex would be appreciated.

4. a program?..ok