(a) Find the general solution for the following linear homogeneous recurrence relation an = 2an−1 + 15αn-2, α0 = 7,α₁ = 25
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- 2. (a) Find the general solution for the homogeneous recurrence bn = 2bn-1 + 3bn-2.Given the first order differential equations, y' + 3xy = 0 (a) Determine the recurrence relation.(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.
- Find the solution of the second order homogeneous recurrence relation:- a + 2a - 3a = 0, n ≥ 2 n-2 M-1 a = 1 With 1a₁₂ = 1 &a₁₂ = 1 2Find the general solutions in powers of x and state the recurrence relation: (2 - x2)y" - xy' + 16y = 03. Find the recurrence relation for y" + 3ry – y = 0. Use the initial conditions y(0) = 2 and y (0) = 0 to find the values the first four non-zero coefficients in y = n=0
- 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.Find f (n) when n = 3k, where f satisfies the recurrencerelation f (n) = 2f (n∕3) + 4 with f (1) = 1.Consider xy"+xy'+2y=0. Find one solution about the regular singular point x = 0 that corresponds to the larger root of the indicial equation. STATE THE RECURRENCE RELATION.
- First derive a recurrence relation giving c for n ≥2 in terms of c) or c₁ (or both). Then apply the given initial conditions to find the values of Co and C₁. Next determine c (in terms of n) and, finally, identify the particular solution in terms of familiar elementary functions. y'' + 4y = 0; y(0) = 0, y'(0) = 1 ... The recurrence relation is = Cn+2 - 4an (n+2)(n+1) for n ≥ 0. (Type an expression using n, C, and Cn +1 as the variables.) The constants are co = 0 and c₁ = 1 (Type integers or fractions.) The explicit formula for the coefficients is C2n = and C2n+1 = for n ≥ 0. The particular solution in terms of elementary functions is y(x) =The recurrence relation for the differential equation xy" +2y - xy = 0 is Oack(k+r) (k+r-1)-Ck-2=0 Obck(k+r+2)(k+r+1) +Ck-2=0 Occk(k+r) (k+r+ 1)² - Ck-2=0 Od.ck(k+r)(k+r-1)+ck-2=0 Oock(k+r)(k+r+1)-k-2=0Given the differential equation: Choose all correct answers. A (x²-1) y" - 6x y¹ + 12y=0 D The recurrence relation is given by: (n-2)(n-3) C C n+2 (n+2) (n+3) n y=c (1+6x4+x³) +c₂(x+x² + x³) (C) y=c (1+6x²+x4) +c₁(x+x³) = The recurrence relation is given by: C n+2 = (n-3)(n-4) (n+1) (n + 2) C n n = 0,1,2,... n=0,1,2,...