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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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)
- |.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd827f080-ccca-4ca0-b441-707814b35224%2F56327da3-6dd2-44d2-8791-d087f04e041b%2F8604ug_processed.png&w=3840&q=75)
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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