Let y' + xºy=0 and let y= 2 Cox". n=0 a Find the recurrence relation of...
1. Let f(n)2 = f(n +1) be a recurrence
relation. Given f(0) = 2, solve.
2. Let
be a recurrence relation. Given f(0) = 1, f(1) = 1 and n 1,
solve.
4. For the equation: y' + x²y = 0, (a) Find the recurrence relation for the coefficients of series solutions about x = 0. (b) Write out the terms to of the general solution.
please use power series
x2 equationx2 -3)y" n+2xy' 0 then the recurrence relation is given by Cn+23(+2) s a power series solution to the differential thisecu0You do not need to calculate this),Given recurrence relation find the general the general solution to this differential you include the "nth" term in your solution.
y"-xy,-у 0, find the recurrence relation for the coefficients of the r series solution aboutx 0. Then find the first six nonzero terms of the particular solution that satisfies y(0) = 1 and y'(0) = 2.
Use the Frobenius method to solve: xy"-2y'+y "=0 . Find index r
and recurrence relation. Compute the first 5 terms a0 −
a4 using the recurrence relation for each solution and
index r.
4 Use the Frobenius method to solve: xy"-2y + y =0. Find index r and recurrence relation. Compute the first 5 terms (a, - a.) using the recurrence relation for each solution and index r.
1. For linear recurrence relation f(n+1) = f(n) + n, find the general solution 2. For linear recurrence relation n = f(n+4) - f(n), find the general solution
consider the DE: y''+x2y'+x2y=0 about the ordinary point x=0 a) find the recurrence relation, and indicate if any of the coefficients are equal to zero .(if any) b) use the recurrence relation to write the first four nonzero terms of each of the two linearly independent power series near the ordinary point x=0. My attempt... after plugging in the y, y' , and y'' power series. I got something that looked like 2a2+6a3x + sigma from n=2 -> to infinity...
Need answers for 1-5
Consider the following recurrence relation: H(n) = {0 if n lessthanorequalto 0 1 if n = 1 or n = 2 H(n - 1) + H (n - 2)-H(n - 3) if n > 2. (a) Compute H(n) for n = 1, 2, ...., 10. (b) Using the pattern from part (a), guess what H(100) is. 2. Consider the recurrence relation defined in Example 3.3 (FROM TEXT BOOK, also discussed in class and shown in slides)...
find a closed form solution to recurrence relation xn
= n for 0
n < m and xn = xn-m+ 1 for n
m discrete math
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(1) Sok power series solution of the forma y(z)-Σ-oanz" to the differential equation: (a) (3 pts) Find recurrence relations for the coefficents, an (b) (4 pts) Use the recurrence relation to give the first three, n-zero terms of the power series solution to the initial value problem: y'-2xy = z, y(0) = 2 (c) (1 pt) Identify the solution as a common function (in closed form).
(1) Sok power series solution of the forma y(z)-Σ-oanz" to the differential equation: (a)...