MATH 20D Lecture 9

$g(t)=k\cos (\omega t)\text{ or }g(t)=k\sin (\omega t)\text{ or both}$

$g(t)=P_n(t)=a_n{t}^n+a_{n-1}{t}^{n-1}+\cdots +a_1(t)+a_0$

Principle of Superposition

Let and be functions. If is a solution to the equation

and is a solution to the equation

then is a solution to the equation

$g(t)=P_n(t)e^{rt}$

Check for conflict with general solution

$g(t)=P_n(t)e^{rt}\cos (\omega t)\text{ or }g(t)=P_n(t)e^{rt}\sin (\omega t)$