(1)Solve a 0 1, and a n 3 a n 1 1 for n 1 using the characteristic equation method Hint Try a n A , a constant, to find a particular solution (2)Solve a 0 1 ,a 1 3 and a n a n 1 6 a n 2 , for n 2 (3) a 0 1 ,a 1 3 and a n a n 1 6 a n 2 1 , for n 2 Hint Use the general solution to the homogeneous problem above, and then try a n A , a constant, to find particular solution

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Question: (1)Solve a 0 = 1, and a n = 3 a n 1 + 1 for n 1 using the characteristic equation method. Hint: Try

(1)Solve a₀= 1, and a_n= 3a_n1+ 1 for n 1 using the characteristic equation method. Hint: Try a_n= A, a constant, to find a particular solution.

(2)Solve a₀= 1,a₁= 3 and a_n= a_n₁+ 6a_n₂, for n 2.

(3)a₀= 1,a₁= 3 and a_n= a_n1+ 6a_n2+ 1, for n 2. Hint: Use the general solution to the homogeneous problem above, and then try a_n= A, a constant, to find particular solution.

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