Final answer:
To find the general solution of the difference equation yₜ₊₂-5yₜ₊₁+6yₜ=3+2t, we use the characteristic equation and solve for the constants to obtain the complete solution.
Step-by-step explanation:
To find the general solution of the difference equation yₜ₊₂-5yₜ₊₁+6yₜ=3+2t, we first need to find the characteristic equation by setting the left side equal to zero: r² - 5r + 6 = 0. This equation can be factored as (r-2)(r-3)=0, which gives us two roots: r=2 and r=3.
The general solution is then given by yₜ = A(2^t) + B(3^t) + C(t), where A, B, and C are constants. To find the particular solution, we substitute yₜ = At + B into the original equation and solve for A and B. Finally, we substitute the values of A and B back into the general solution to get the complete solution.