# Lab 8 - verify that c is arbitrary in this case y – xy =...

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MATH 342 Differential Equations with Linear Algebra II Fall 2009 Due November 2, 2009 Homework 8 Section 8.2 1. Page 527, number 26 2. Page 527, number 27 3. Page 527, number 30 4. The equation y" - 2xy' + λy = 0 -∞ < x < ∞ where λ is a constant, is known as the Hermite equation which is an important equation in mathematical physics. Find the first four terms in each of the two solutions about x = 0. 5. Solve the differential equation by a series in powers of x and

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Unformatted text preview: verify that c is arbitrary in this case. y' – xy = 0 Section 8.3 6. Page 543 numbers 4 and 7 7. Page 543 number 13 8. Page 543 number 24 9. Page 543, number 30 10. The Laguerre differential equation is: x 2 y" + xy' + x 2 y = 0 a) Show that x = 0 is a regular singular point. b) Determine the indical equation, its roots and the recurrence relation. c) Find one solution (x > 0). Show that if λ = m, a positive integer, this solution reduces to a polynomial....
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## This note was uploaded on 12/23/2009 for the course MATH 342 taught by Professor Edwards,d during the Fall '08 term at University of Delaware.

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Lab 8 - verify that c is arbitrary in this case y – xy =...

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