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y(n+2)+y(n+1)-6y(n) equation

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Numerical solution:

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The solution

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y*(n + 2) + y*(n + 1) - 6*y*n = 0
$$- n 6 y + \left(y \left(n + 1\right) + y \left(n + 2\right)\right) = 0$$
Detail solution
Given the linear equation:
y*(n+2)+y*(n+1)-6*y*(n) = 0

Expand brackets in the left part
yn+2+yn+1-6*yn = 0

Looking for similar summands in the left part:
y*(1 + n) + y*(2 + n) - 6*n*y = 0

Divide both parts of the equation by (y*(1 + n) + y*(2 + n) - 6*n*y)/y
y = 0 / ((y*(1 + n) + y*(2 + n) - 6*n*y)/y)

We get the answer: y = 0
The graph
Rapid solution [src]
y1 = 0
$$y_{1} = 0$$
y1 = 0
Sum and product of roots [src]
sum
0
$$0$$
=
0
$$0$$
product
0
$$0$$
=
0
$$0$$
0