Hello everyone,

I have this problem

$a_n + a_{n-1} + 6a_{n-2} = 5n(-1)^n + 2^n$

This is the given solution: \(\displaystyle a_n = (\sqrt{6})^n(C_1\cdot \sin\phi n + C_2\cdot \cos\phi n) + \frac{1}{3} \cdot 2^n + \left(\frac{5}{6}\cdot n + \frac{55}{36}\right)(-1)^n\)

I used the discriminant to find the zeros of characteristic polynomial but then I got this:

\(\displaystyle x_{1,2} = -1 \pm \frac{\sqrt{1-24}}{2}\)

and have no idea how to continue.:cry:

Can someone please help me solve this step by step?

Thanks in advance.

I have this problem

$a_n + a_{n-1} + 6a_{n-2} = 5n(-1)^n + 2^n$

This is the given solution: \(\displaystyle a_n = (\sqrt{6})^n(C_1\cdot \sin\phi n + C_2\cdot \cos\phi n) + \frac{1}{3} \cdot 2^n + \left(\frac{5}{6}\cdot n + \frac{55}{36}\right)(-1)^n\)

I used the discriminant to find the zeros of characteristic polynomial but then I got this:

\(\displaystyle x_{1,2} = -1 \pm \frac{\sqrt{1-24}}{2}\)

and have no idea how to continue.:cry:

Can someone please help me solve this step by step?

Thanks in advance.

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