Solve the initial-value problem y" + xy' + y = 0, y(0) = 0, y'(0) = 1 in the form of a power series in powers of x.(- 1)" 2n n! x2n + 1O A. y = >(2n + 1)!n=0(- 1)A 2ª (n + 1)! x2n +1(2n + 1)!O B. y = >n=0(-1)" 2n +1 n! x 2n + 1(2n + 1)!O C.y = >n=0(- 1)n+1 2n n! x2n + 1O D. y = >(2n + 1)!n=0(- 1)a 2º (n - 1)! x2n + 1E. y = >n=0(2n + 1)!

given initial value problem y''+xy'+y=0 ...i with y0=0 , y'0=1 find the solution in the…

Answered: Solve the initial-value problem y" + xy…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find a general solution in powers of x of the differential equation. State the recurrence relation and the guaranteed radius of convergence. (x²-9) y' + 4xy' + 2y = 0 The recurrence relation is C₁ +2 Find a general solution in powers of x. y(x) = (Type an expression in terms of co and c₁. Type any series in summation notation using n as the index variable and 0 as the starting index.) Find the guaranteed radius of convergence p. p= Find a general solution in powers of x of the differential equation. State the recurrence relation and the guaranteed radius of convergence. (x²+25) y" +6xy' + 4y = 0 The recurrence relation is Cn +2 = Find a general solution in powers of x. y(x) = (Type an expression in terms of co and c₁. Type any series in summation notation using n as the index variable and 0 as the starting index.) Find the guaranteed radius of convergence p. p=
2x(x-1)y"-(X+1)y'+y=0, develope the series solution by frobenit's method.
Assume y(x) = ax" for #2, 3, 4, 5 n=0 5. Find at least the first four nonzero terms in a power series expansion of the I.V.P. y'-e'y=0; y(0)=1 1
Consider a series solutions about the point x = 0 for the ODE: y" - xy + xy = 0 (i) Find a recurrence relationship for the coefficients of the series. (ii) Using (i) to evaluate the first four non-zero terms of each of the two linearly independent solutions and state the general solution for y(x).
Use power series to solve the initial-value problem (x² – 2)/" + 10xy + 8y = 0 , y(0) = 1, y (0) = 0 . Answer: y = > 1 a2n +> x2n+1. n=0 n=0
If f(x) = 00 n=0 n n² + 1 n=0 (f(x) + g(x)). n -x" and g(x) = Σ ( − 1)″- -", find the power series of n² + 1 n=0
Use the power series method to find a general solution to the problem (x-1)y'' + y' =0
find the power series solution of, xy''+(1-x)y'-y=0 at its regular-singular point.
The second order equation 81a?y" + 81ry' + (81x? – 16) y = 0 has a regular singular point at a = 0, and has series solutions of the form 00 (1) Insert the formal power series into the differential equation, we derive an equation Cn+ n-2 So we have the indicial equation and a recurrence relation Cn_2 for n = 2, 3, . (2) From the indicial equation we can solve the indicial roots (enter your results as a comma separated list). For any one of the indicial roots, we have c = (3) Let r, be the smaller indicial root. Then r and the recurrence relation becomes Cn 2 for n = 2, 3, - . . Let co =1 From the recurrence relation, we have a solution I+1+ z+2+ T+3+ z+4+ +... Y1 = z+ (4) Let r2 be the larger indicial root Then T2 = and the recurrence relation becomes Cn= Cn 2 for n = 2, 3, -.. Let co = 1 From the recurrence relation, we have another solution. 2 = 1+ T+2+ Ta+0 +... (5) The general solution is given by y = Ay + By, with arbitrary constants A, B.

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