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Let y be a function of x & z is a real constant. Find the series solution of (x²-z) y"+8xy'+10 y=x (table in front cover of textbook)

Let y be a function of x & z is a real constant. Find the series solution of (x²-z) y"+8xy'+10 y=x (table in front cover of textbook)

Advanced Engineering Mathematics
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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Let y be a function of x & z is a real constant. Find the series solution of (х-2) у"+8ху'+10 у%3Dх (table in front cover of textbook)
Transcribed Image Text:Let y be a function of x & z is a real constant. Find the series solution of (х-2) у"+8ху'+10 у%3Dх (table in front cover of textbook)
Table of Laplace Transforms This table summarizes the general properties of Laplace transforms and the Laplace transforms of particular functions derived in Chapter 10. Function Transform Function Transform F(s) af(t) + bgt) a F(s) + bG(s) sF(s) – S(0) cos kt s? F(s) – sf(0) – f'(0) sin kt " F(6) - "- s(0) – -..- f(a-1)(0) cosh kt F(s) sinh kt s2 -k2 S-a F(s -a) cos kt (s-a)? + u(t -a) f -a) ea F(s) at sin kr (s-a) + sgt - 1)dr F(s)G(s) 23 (sin kt - kt cos kt) -F'() sinkt (5² + k²jZ (-1)" F(6)(s) (sinkt + kt cos kt) 2k F(a) da M(t - a) S). period p S -a) (-1)6/a] (square wave) as 1 tanh (staircase) s(1 -ar) Г(а + 1) - |.
Transcribed Image Text:Table of Laplace Transforms This table summarizes the general properties of Laplace transforms and the Laplace transforms of particular functions derived in Chapter 10. Function Transform Function Transform F(s) af(t) + bgt) a F(s) + bG(s) sF(s) – S(0) cos kt s? F(s) – sf(0) – f'(0) sin kt " F(6) - "- s(0) – -..- f(a-1)(0) cosh kt F(s) sinh kt s2 -k2 S-a F(s -a) cos kt (s-a)? + u(t -a) f -a) ea F(s) at sin kr (s-a) + sgt - 1)dr F(s)G(s) 23 (sin kt - kt cos kt) -F'() sinkt (5² + k²jZ (-1)" F(6)(s) (sinkt + kt cos kt) 2k F(a) da M(t - a) S). period p S -a) (-1)6/a] (square wave) as 1 tanh (staircase) s(1 -ar) Г(а + 1) - |.
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