Hi, I have this initial value problem: f''(x)+4f'(x)+5f(x)=0 with f(0)=1 and f'(0)=-2
I need to show that f(x)=cos(x)/e^2x is a solution to this initial value problem.
then find the domain of this solution..
Pls help, thanks!
$\displaystyle f(x) = cosx \times e^{-2x}$
Thus
$\displaystyle f'(x)= (-sinx \times e^{-2x}) + (cosx \times -2e^{-2x}) $
$\displaystyle f''(x) = (2e^{-2x} sinx- e^{-2x}cosx) +
(2e^{-2x} sinx + 4e^{-2x} cosx)$
$\displaystyle f''(x) = 4e^{-2x}sinx - 3e^{-2x} cosx $
now you can find compute it for the IVP