Question

这道题谁会？？？？？

这道题谁会？？？？？差分方程，表示不会

Answer 1

y(n+1) -2yn = 3n^2
y(n+1)+ k1.(n+1)^2 +k2.(n+1) +k3. = 2( yn + k1.n^2+k2.n + k3)
coef. of n^2
k1 =3
coef. of n
k2 - 2k1 = 0
k2=6
coef. of constant
k3 - k2 -k1 =0
k3-6-3=0
k3=9
y(n+1) -2yn = 3n^2
y(n+1)+ 3(n+1)^2 +6(n+1) +9 = 2( yn + 3n^2+6n + 9)
=> {yn + 3n^2+6n + 9} 是等比数列, q=2
yn + 3n^2+6n + 9 =2^(n-1) .(y1 + 3+6 + 9)
yn = -(3n^2+6n + 9) + (y1+18).2^(n-1)