Hello, I was trying to solve the following defferential equation and stuck after the homogeneous solution.

The equation is un = 2√2un−1 − 4un−2 + √2n u0 = 5, u1 = √2;

My Way I tried is 1st, characteristic polynomial x^2-4x+2√2,

Then the homogeneous general solution un=A(-2+(√4+(2√2))+B(-2-(√4-(2√2)), ok here is I hit the wall, pls help