此差分方程的待征方程为 [tex=5.429x1.357]Kc5tTu4tcMe+Fo662Zl20hsTnci/FJQNBcnhst5tlHo=[/tex], 解得特征根 [tex=4.714x1.214]5S71iLPHMsGQxItA2oTHqXkSEgJKppz5aDTdn/HRMmw=[/tex] 。 [br][/br]其齐次解[p=align:center][tex=7.5x1.357]CUVlelY+Q8bh6yiA+jD6wG3ptrgXDMgUVEIC7kKE+kuD1x6z6lAMLmk52JjVabsY[/tex]设特解 [tex=5.214x1.357]1qJkSNwgH3lERfFmOq2/ijT/3sEVaKOI61b61vR3zuU=[/tex], 代入方程, [tex=18.643x2.357]O4uBpCX6AO/8p3gOqni6qMUYgas7IIKguiQoewtFX3sqKCmhH1n0PXo4hFyrsiGnr+SaysTj0quv2vyZWooTawHwibUfLrqH1Ov3i9p+BoqS8EXp/uMXXuNxI3CgRfORx+dj69dS4NSghLuH07EuhA==[/tex][p=align:center][tex=11.214x2.357]MtHOqW0UQy5v5/RaoTZnRFzWwswW+PtZL9PCOxRcfe6WNRZIrvUDFLHHImnhbSHDxSMACXx0WFwU5FtdmkRa5g==[/tex]初始条件 [tex=18.929x3.357]7EJHVCtO2IWq3KpdB+jQsvshwCfL6sGHHt/a3ZLmgy/tC0SnD9gnPWgcXpLGk+R3rT1MksmdMXd/FQ6RjC0DAM3w2nrgUSOeM826lC3w+H1ZfZ4iCiwVK+vaG2Jsx0AnsmGryR5VzBajSuBlPaYHYA==[/tex]$$ \left.\begin{array}{c} y(0)=-10 \\ y(1)=-49 \end{array}\right\} \Rightarrow\left\{\begin{array} { c } { \frac { 2 } { 1 5 } + k _ { 1 } + k _ { 2 } = - 1 0 } \\ { \frac { 1 } { 1 5 } + 2 k _ { 1 } + 3 k _ { 2 } = - 4 9 } \end{array} \Rightarrow \left\{\begin{array}{l} k_{1}=16 \\ k_{2}=-\frac{126}{5} \end{array}\right.\right. $$y(n)=\left[\frac{2}{15} \cdot 0.5^{n}+\frac{56}{3} \cdot 2^{n}-\frac{144}{5} \cdot 3^{n}\right] u(n)