Question 8Given the differential equation:AB(1+x2) y + 2xy - 2y=0y=c,(1+x arctan(x)) +cThe recurrence relation is given by:3n+27 (₁)11The recurrence relation is given by:1-n1+n+27(-y=carctan(x) +c₁x²1+nn=0,1,2,...n=0,1,2,...

Recurrence relation of differential equation using power series

Answered: Question 8 Given the differential…

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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Example 9. Prove that g(x) ex (cos ex - ex sin e) is the solution of %3D the integral equation g(x) = (1 - xe2x) cos 1- e2x sin 1 + [1-(x- t)e2x1 g(t) dt %3D
Question 5 Solve x4y (4) + 6x³y (3) + 25x2y + 19xy' + 81y=0 where x > 0 c cos (3lnx) +c sin (31nx) +c cos(x) Inx+c sin(x) Inx c cos (3lnx) +c sin (3lnx) +c cos (3lnx) Inx+c sin (3/nx) Inx 4 c cos (3lnx) +c sin (3lnx) + c¸cos (3lnx) +c_sin (3/nx) c cos (31nx) +c_sin (3x)+c cos(x) Inx+c sin (3lnx) Inx
Given the following linear system of ODE: V₁' = 4V1 +2V2 V₂' = 10/₁-4/2 Solve the initial value problem, given y₁ (0) = 1 and y₂ (0) = 2 O y = 7/6 O y = et + O --8--8- H y [1] H y=-1 ebt = [2] e e³t+5/6 -¹ [He y = 1/6 L - 1/6 [15] ebt + 23 -6t 5 e-6t e-3t e-ot 1/6[1]eºt +5/6 [11/5] 0 e h -6t
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ΕΧΑPLE 8.1.1 Evaluate (ax +b)" dx, assuming that a and b are constants, a + 0, and n is a positive integer. We let u = ax + b so du = a dx or dx = du/a. Then 1 n du a(n + 1) 1 (ax + b)"+1 + C. (ах + b)" dx %3 u' +C = a(n + 1)
sin x - X dx = ? 0. 22n (2n).(2n)! (a) (-1)" 22n+2 (2n +2).(2n +2)! (b) (-1)" n=1 n=1 (c) M(-)" 22n+1 (2n +1).(2n +1)! 22n-1 (2n-1).(2n-1)! (d) (-) n=1 n=1 (e) n.n! n=1 Seçtiğiniz cevabın işaretlendiğini görene kadar bekleyiniz. Soruyu boş birakmak isterseniz işaretlediğiniz seçeneğe Aramak için buraya yazın ** F11 F10 F9 F8 F7 F6 F5 F4 F3 & 10 8 C9 4 %24 5 6 3 # U T K G H. 团 R
= 1) The function f(x) periodic on the interval [0, 2л] has complex Fourier series f(x): Σ(1/n²) einx where the sum over n goes from - infinity to infinity. Convert this to cosine and sine Fourier Series by finding the values of A's and B's in the expression Ao + ΣAn cos(nx) + Σ Bn sin(nx) where each sum goes from 1 to infinity. Hint: consider the n and -n term together in the complex Fourier Series or use Euler's identity.
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= - [cos(x + n) + cos(x − ñ)] [(cos(x) cos(π) - = = || II - I 1/1/[(-COS(X) - 2 ) + + cos(x) cos(T) + + (−cos(x) + )]
Question 19 Find the Taylor polynomial P5(x) centered at x = 0 for the function f(x) = 4x cos (x²) 1 a) -x - b) О-2х3 + 4х c) O2x + x d) O-x – 4x e) O2x + 4x

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Question 8 Given the differential equation: A y=c,(1+x arctan(x)) +c Ⓡ (1+x2) y + 2xy - 2y=0 The recurrence relation is given by: y=co *+27(- Ca The recurrence relation is given by: *+2=(- arctan(x) +c rẻ 1+n 1-n n -) c 1+n n=0,1,2,... n=0,1,2,...

Question 8 Given the differential equation: A y=c,(1+x arctan(x)) +c Ⓡ (1+x2) y + 2xy - 2y=0 The recurrence relation is given by: y=co +27(- Ca The recurrence relation is given by: +2=(- arctan(x) +c rẻ 1+n 1-n n -) c 1+n n=0,1,2,... n=0,1,2,...