Compute the general solution valid near the origin ((+4x² )y" - By = O 'y= s{1 - 4x°) + a»\x= 22kx2k+1 k=1 4k2 – 1 (-1)**'22kx2k+1 °y=aol1 + 4x°) + as x + y=ag{1=4x°) + a;[x* Z; 4k? – 1 "r (-1)*22kx2k+1 4k? – 1 224, 24 +1 y=a,(1+4x?) +ax- 4k2 -1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
100%
Compute the general solution valid near the origin
(1+4x² )y" - By = 0
y=og{1 -4x°) + as x-
° y=ag{2 + 4x°) + as[x* Z
y=ag{1-4x°) + a_\** Z;
22k x2k+1
4k? – 1
k=1
(-1)**'22kx2k+1
4k? - 1 "r
(-1)*22kx2k+1
4k² – 1
azx + E
224, 2k +
y=a,(1+4x*) +a =
4k2 – 1
Transcribed Image Text:Compute the general solution valid near the origin (1+4x² )y" - By = 0 y=og{1 -4x°) + as x- ° y=ag{2 + 4x°) + as[x* Z y=ag{1-4x°) + a_\** Z; 22k x2k+1 4k? – 1 k=1 (-1)**'22kx2k+1 4k? - 1 "r (-1)*22kx2k+1 4k² – 1 azx + E 224, 2k + y=a,(1+4x*) +a = 4k2 – 1
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,