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+y
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)
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.
求满足下列条件的微分方程,并给出通解:
(1)未知方程为二阶非齐次线性方程,且有3个特解:
(2)未知方程为二阶常系数非齐次线性方程,有两个特解
(3)未知方程有特解。
求下列二阶线性齐次差分方程的通解或特解:
(1)yn+2+3yn+1-10yn=0;
(2)yn+2+2yn+1-8yn=0;
(3)yn+2-yn=0;
(4)yn+2+yn=0;
(5)yn+2-2yn+1+5yn=0;
(6)4yn+2-12yn+1+9yn=0;
(7)yn+2-2yn+1-3yn=0;
(8)yn+2-2yn+1+yn=0,y0=1,y1=2。
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.
求下列二阶常系数线性齐次微分方程的通解和特解。y“-5y'+6y=0,y|x=0 ,y'(0)=1