How are the constant alphas in these simultaneous equations 1, 3 and -2?

[yakin]

The book answer is 1, 3 and -2. I can't figure how they got it? Please help to understand and help me to get through where i got stuck.

Please look at images from bottom page to top page(where you see crossing on a page)

 

[MarkFL]

You have correctly found that the characteristic root is $r=-1$ of multiplicity 3, however, you have not properly dealt with the fact that the root is repeated. Since this root is of multiplicity 3, the closed-form will be:

$$a_n=c_1(-1)^n+c_2n(-1)^n+c_3n^2(-1)^n=(-1)^n\left(c_1+c_2n+c_3n^2 \right)$$

 

[yakin]

Thank you for your feedback. I noticed that. I forgot to stick "n" in the general form of the solution with the repeated roots. Thanks though!

Question: How do you write maths directly with correct notation here? I have to take pics of my work and then upload the pics.

 

[MarkFL]

...
Question: How do you write maths directly with correct notation here? I have to take pics of my work and then upload the pics.

We have $\LaTeX$ implemented here to allow writing mathematical expressions.

Here is a link to a thread containing a pdf tutorial written by one of our staff:

http://mathhelpboards.com/latex-tips-tutorials-56/math-help-boards-latex-guide-pdf-1142.html