Find the general solution for the following linear homogeneous recurrence relations: (a) an = 2an-1 + 15an-2 (b) an = -12an-1 - do 36an-2, ao = 9, a₁ = 18
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- (a) Give the general form of a linear homogeneous recurrence equation whose characteristic equation (after factoring) is (x+3)²(x - 2)²(x − 6) = 0. Justify your answer.8. Consider the second-order homogeneous recurrence relation an = 3an-1 + 10an-2 with initial conditions ao = 5, a1 = 11. (a) Find the next three terms of the sequence. (b) Find the general solution. (c) Find the unique solution with the given initial conditions.Use the method of Frobenius to find the recurrence relation for the following equations: d²y 1. x(1– x)- 2 + 2y = 0 2. x+ (1 – 2x)- y = 0 dx² d?y dx2