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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Solve the initial-value problem (x2 - 1)y" + xy' - y = 0, y(0) = 1, y'(0) = 0 in the form of a power series in powers of x. (2n - 2)! O A. 1+ ) 22n - 1 x2n n!(n - 1)! n=1 (2n - 2)! x2n 22n - 1 n!(n + 1)! B. 1- ) n=1 (2n - 2)! x2n 22n - 1 n!(n - 1)! O C. 1- > n=1 (2n - 1)! D. 1- > 22n - 1 x2n n!(n - 1)! n=1 (2n - 2)! x2n 22n - 1 n!(n + 1)! O E. 1+ > n=1
Find the series solution of y"+ (1+x²)y=0 using the power series method.
Solve for the general solution using the Power Series. The answer was already given, you just have to provide the solutions. Find the G.S. about xo = 0 for the following DE's 2. (1+x²)y" + 10xy' + 20y = 0 (−1)k(k+ 1)(k+ 2)(2k + 3) a₁x²k+1 Answer: y = a₁ + a₂x + Σ (-1)* (2k + 1)(2k + 3)(k + 1) qx²k. 3 6 k=1 k=1
Which of the following power series must be used as the nonhomogeneous part for the given initial value problem y" -y + (z+ ¥)"y = In ( + 피) y (-) = 1, y (-}) = 0 in order to obtain the solution by power series solution method? A) -1)" (z – 4)" B) -1)* (2)m (-1)"+1 (2r + 1)" 0 n! D) E1)"- (r+ 4)" (-1)" " E) > 2" (n + 1) n=1
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=
(-1)"(2-5-8. (3n+2))(x-1)2n+2 3n. (n2 +1) The derivative of the power series f(x) = 2 is (- 1)"(2 -5-8 (3n+2))(2n+2)(x- 1)2n+1 3n. (n² +1) %3D n=0 True False Click Save and Submit to save and submit. Click Save All Answers to save all answers.
(1₁ y = I se power series to solve the initial-value problem C n=0 2n + XO 70 n=0 2n+1 (x²2)y" + 10xy' + 8y = 0, help (formulas) y(0) = 1, y' (0) = 0.
Choose the power series solution to y" - 4xy + (4x² - 2)y = 0. ○ (ao +α1x)ex² O None ○ (a + α1x)ex²
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).
1. Which of the following power series must be used as the nonhomogeneous part for the given initial value problem { y" – y + (x + }) y = In ({ + x) y (-}) = 1, y' (-}) = 0 in order to obtain the solution by power series solution method? A) -1)" (x – )" (-1)"+1 (x)" B) (-1)"+1 (2x + 1)" n! n=0 n=1 n=0 (-1)"-' (x + })" (-1)" x" E) 2" (n + 1) n=1 n=1
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Use the power series method to find a general solution to the problem (x-1)y'' + y' =0

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