Thread: solving inhomogenous linear difference equations

Solve the following inhomogeneous linear difference equation: Yk+3 + 5Yk+2 - 2Yk+1 - 6Yk = 32k + 6. Use Yk=Ak+b to solve for A and B.

So far I have followed my notes and have got
A(k+3)+B+5A(k+2)+5B+(-2)A(k+1)+(-2)B-6A(k)-6B=32k+6
then
Ak+3A+b+5Ak+1-A+5B-2Ak-2A-2B-6Ak-6B=32K=6
That is where my notes end for this. Exept we solve for the constant of K. How do I find A and B from here?

Originally Posted by brokenflower66

Ak+3A+b+5Ak+1-A+5B-2Ak-2A-2B-6Ak-6B=32K=6

I'll start here and assume this equation is correct. Your equation simplifies to


Now match terms. -2A = 32 and -2B = 6.

By the way Mathematics is case sensitive. So B is not in general equal to b, and K is not the same as k.

-Dan