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Math Help - solving inhomogenous linear difference equations

  1. #1
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    Question 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?
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  2. #2
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    Quote Originally Posted by brokenflower66 View Post
    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
    -2Ak -2B = 32k + 6

    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
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