Show CO PLETE solutions. 1) Show that Laguerre's ODE, Table 7.1, may be put into self-adjoint form by multiplying by ex and that w(x) = e* is the weighting function.
Show CO PLETE solutions. 1) Show that Laguerre's ODE, Table 7.1, may be put into self-adjoint form by multiplying by ex and that w(x) = e* is the weighting function.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Table 7.1 Singularities of Some Important ODES.
Equation
1. Hypergeometric
x(x - 1)y" + [(1 +a+b)x+c]y' + aby = 0
2. Legendre
(1-x2)y" - 2xy' +1(1+1)y=0
3. Chebyshev
(1-x²)y" - xy + n²y=0
4. Confluent hypergeometric
xy" +(c-x)y'-ay=0
5. Bessel
x²y" + xy + (x²-n²)y=0
6. Laguerrea
xy" + (1-x)y' + ay = 0
7. Simple harmonic oscillator
y"+w²y=0
8. Hermite
y"-2xy + 2ay=0
"The associated equations have the same singular points.
Regular
Singularity
x =
0,1,00
-1, 1,00
-1, 1,00
0
Irregular
Singularity
x =
:
8 8 8 8 8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2bdc46f7-0885-4700-8887-6851601eff03%2Fb06343e0-a6dd-4a0f-a5da-2d58c139552f%2Fxwcxha8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Table 7.1 Singularities of Some Important ODES.
Equation
1. Hypergeometric
x(x - 1)y" + [(1 +a+b)x+c]y' + aby = 0
2. Legendre
(1-x2)y" - 2xy' +1(1+1)y=0
3. Chebyshev
(1-x²)y" - xy + n²y=0
4. Confluent hypergeometric
xy" +(c-x)y'-ay=0
5. Bessel
x²y" + xy + (x²-n²)y=0
6. Laguerrea
xy" + (1-x)y' + ay = 0
7. Simple harmonic oscillator
y"+w²y=0
8. Hermite
y"-2xy + 2ay=0
"The associated equations have the same singular points.
Regular
Singularity
x =
0,1,00
-1, 1,00
-1, 1,00
0
Irregular
Singularity
x =
:
8 8 8 8 8
![Show CO PLETE solutions.
Show that Laguerre's ODE, Table 7.1, may be put into self-adjoint form by
multiplying by e* and that w(x) = e* is the weighting function.
1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2bdc46f7-0885-4700-8887-6851601eff03%2Fb06343e0-a6dd-4a0f-a5da-2d58c139552f%2Ftnz5eel_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Show CO PLETE solutions.
Show that Laguerre's ODE, Table 7.1, may be put into self-adjoint form by
multiplying by e* and that w(x) = e* is the weighting function.
1)
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