this should be simple but I can't get it to come out right
i have the general solution as x(t)= C1e^(-t)cos4.36t + C2e^(-t)sin4.36t
can someone get the first deriv of x(t)? C1 and C2 are what I need to solve for to find the particular solution
this should be simple but I can't get it to come out right
i have the general solution as x(t)= C1e^(-t)cos4.36t + C2e^(-t)sin4.36t
can someone get the first deriv of x(t)? C1 and C2 are what I need to solve for to find the particular solution
Hello chief27I agree with your general solution. I've left the term as $\displaystyle \sqrt{19}$ rather than 4.36.
$\displaystyle x = e^{-t}(C_1\cos\sqrt{19}t+C_2\sin\sqrt{19}t)$
$\displaystyle \Rightarrow x(0) = C_1 = 1$
$\displaystyle \Rightarrow x = e^{-t}(\cos\sqrt{19}t+C_2\sin\sqrt{19}t)$
$\displaystyle \Rightarrow \dot{x} = e^{-t}(-\sqrt{19}\sin\sqrt{19}t + \sqrt{19}C_2\cos\sqrt{19}t) - e^{-t}(\cos\sqrt{19}t+C_2\sin\sqrt{19}t)$
$\displaystyle \Rightarrow \dot{x}(0) = \sqrt{19}C_2 - 1 = 0$
$\displaystyle \Rightarrow C_2 = \frac{1}{\sqrt{19}}$
$\displaystyle \Rightarrow x = e^{-t}\left(\cos\sqrt{19}t+\frac{1}{\sqrt{19}}\sin\sqr t{19}t\right)$
Grandad