求下列二阶线性非齐次差分方程的通解或特解:
(1)yn+2-10yn+1+25yn=2n;
(2)yn+2+4yn+1-5yn=2n-3;
(3)yn+2-3yn+1+2yn=1-2n;
(4)yn+2+4yn+1+4yn=(-2)n(n+1);
(5)yn+2-10yn+1+25yn=3n+2n+5;
(6)
已知某二阶常系数非齐次线性差分方程的通解为
yx=C1+C2(-2)x+3x,
求此差分方程.
求下列二阶齐次线性差分方程的通解或满足条件的特解: (1)yn+2-7yn+1+12yn=0; (2)yn+2=yn+1+yn; (3)yn+2-6yn+1+9yn=0; (4)yn+2+4yn=0; (5)yn+2-4(a+1)yn+1+4a2yn=0,a为常数,1+2a>0; (6)yn+2+2yn+1-3yn=0,yo=-1,y1=1.
求下列差分方程的通解: (1)2yn+1+yn=3+n; (2)yn+1-2yn=2n; (3)yn+1-αyn=eβn,α,β为常数,α≠0.
求下列二阶常系数非齐次线性差分方程的通解或在给定的初始条件下的特解:
yx+2+yx+1-2yx=12,y0=0,y1=0.
按要求求下列一阶差分方程的通解或特解. (1)求yx+1-2yx=2x的通解; (2)求yx+1一2yx=3x2满足条件yx(0)=0的解; (3)求2yx+1+10yx一5x=0的通解.