# Difference equation, ypn guess problem

1. Jan 1, 2012

### toofle

1. The problem statement, all variables and given/known data
Solve the difference equation

2. Relevant equations
y[n+2]-3y[n+1]+2y[n]==4n*2^n, n>=0
y0=0,y1=1

3. The attempt at a solution
1. Homogenous solution:
Characteristic equation => r^2-3r+2==0 <=> r1=1,r2=2 => yhn = C1*1^n+C2*2^n

2. Particular solution:
ypn = ?
I tried different things but everything comes out wrong.

I guess(what is the right word?) witha polynomial of the same degree as the right hand side of the equation how is it when 2^n is in both yhn and righthand side of the equation?

2. Jan 2, 2012

### The1337gamer

Try ypn = bn(2^n). b is a constant to be found

Notice in the complimentary function, (2^n) is multiplied by just a constant, this is different to the form of the particular solution as the RHS contains a non-zero first degree polynomial multiplying (2^n).

But let's say for example your complementary function included a term cn(2^n) and the RHS = 4n(2^n) then for the particular solution we would try: Bn^2(2^n) so a 2nd degree polynomial multiplying 2^n