Question

求解！！！急！！！

求解！！！急！！！

Answer 1

y'-3y=9+4sint
let
yp= Acost +Bsint +C
yp'= -Asint +Bcost
yp'-3yp=9+4sint
-Asint +Bcost +(-3Acost -3Bsint -3C) =9+4sint
(-3A+B)cost +(-A-3B)sint -3C =9+4sint
C=-3
-3A+B=0 (1)
-A-3B=4 (2)
3(2)+(1)
-6A =12
A=-2
from (1)
-3A+B=0
B=-6
yp= -2cost -6sint -3
The aux. equation
p-3=0
p=3
let
yg= De^(3t)
y= yg+yp = De^(3t) -2cost -6sint -3
y(0)= D -2 -3 = D-5 =k
=>y0=k >0 ( k 是一个常数）