The characteristic equation r2−3r+2=0r^2 - 3r + 2 = 0r2−3r+2=0 has roots r1=2r_1 = 2r1=2 and r2=1r_2 = 1r2=1. The general solution is:
an=c1⋅2n+c2a_n = c_1 \cdot 2^n + c_2an=c1⋅2n+c2
an=(c1+c2n)⋅2na_n = (c_1 + c_2 n) \cdot 2^nan=(c1+c2n)⋅2n
an=c1⋅2n+c2a_n = c_1 \cdot 2n + c_2an=c1⋅2n+c2
an=c1⋅2n⋅c2na_n = c_1 \cdot 2^n \cdot c_2^nan=c1⋅2n⋅c2n