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Activity 5.6 1. Obtain the general solution of the given ODE on (0,00). (a) x²y" + xy + (x² - ) y = 0

Activity 5.6 1. Obtain the general solution of the given ODE on (0,00). (a) x²y" + xy + (x² - ) y = 0

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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Type here to search 1. Obtain the general solution of the given ODE on (0,00). (a) x²y" + xy' + (x² − ) y = 0 (b) 4x²y" + 4xy' +(4x²25)y = 0 (c) x²y" + xy + (x² − 1)y = 0 (d) x²y" + xy' + (9x² − 4)y = 0 (e) x²y" + xy' + (25x² ) y = 0 (f) x²y" + xy' + (36x² - 1) y = 0 2. (a) Use the explicit solutions y₁ (x) and y2(x) of Legendre's equation and the appropriate choice of Co and C₁ to determine the Legendre poly- nomials Pº(r) and P7(X). (b) Write down the differental equations for which P(x) and P7(x) are particular solutions. 3. Use the recurrence relation and Po(x) = 1, P₁(x) = x to generate the next 6 Legendre polynomials. À a W O g 13°C Activity 5.6 BE hp
Transcribed Image Text:Type here to search 1. Obtain the general solution of the given ODE on (0,00). (a) x²y" + xy' + (x² − ) y = 0 (b) 4x²y" + 4xy' +(4x²25)y = 0 (c) x²y" + xy + (x² − 1)y = 0 (d) x²y" + xy' + (9x² − 4)y = 0 (e) x²y" + xy' + (25x² ) y = 0 (f) x²y" + xy' + (36x² - 1) y = 0 2. (a) Use the explicit solutions y₁ (x) and y2(x) of Legendre's equation and the appropriate choice of Co and C₁ to determine the Legendre poly- nomials Pº(r) and P7(X). (b) Write down the differental equations for which P(x) and P7(x) are particular solutions. 3. Use the recurrence relation and Po(x) = 1, P₁(x) = x to generate the next 6 Legendre polynomials. À a W O g 13°C Activity 5.6 BE hp
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