Recurrence relation $$a_n = 2 a_{n-1} - a_{n-2} + 3$$ ?
The initial conditions are $a_0$ = 2 and $a_1$ = 5.
I know the characteristic equation is: $$t^2-2t+1$$ The roots are 1 and 1.
The homogeneous part is: $$( c_1 + c_2 * n ) * 1^n$$
How do you solve the particular part?
I guess the particular part to be: A
I substituted in recurrence relation: A = 2A - A + 3 but I get A = A+3 --> 0 = 3.
What did I do wrong?
Because this is a "failure case" you have to try $c_3n^2$ for the particular solution, since both $c_1$ and $c_2n$ are already "taken".
On substitution you will find that $c_3=\frac32$, and hopefully you can continue from there...