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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
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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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
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)
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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