HW3 - X n =1 (-1) n (1-n ) 2 n n ! = 3 2 e-1 / 2-1 . 5. (5...

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MAE 294A / SIO 203A – Introduction to Applied Mathematics I – Fall 2009 Homework # 3 Assigned: October 15 2009 Due: October 22 2009, in class. 1. (5 points) Solve the following eigenvalue problem on the domain [0 ,L ] y 00 + Ey = 0 , y (0) = 0 , y 0 ( L ) + y ( L ) = 0 . 3. (4 points) Classify all the singular points (finite and infinite) for the spheroidal wave equation (1 - x 2 ) y 00 - 2 xy 0 + λ + 4 θ (1 - x 2 ) - μ 2 1 - x 2 ! y = 0 , for all values of the parameters λ , θ , and μ . 4. (5 points) Obtain the series solution to the initial value problem y 0 + y = e - x , y (0) = 1 . By comparing this with the direct solution of the differential equation, show that
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Unformatted text preview: X n =1 (-1) n (1-n ) 2 n n ! = 3 2 e-1 / 2-1 . 5. (5 points) We consider the following initial value problem (1-x 3 ) y 00-6 x 2 y-6 xy = 0 , with y (0) = 1, y (0) = 0. Find a series solution for y . Sum the series and verify that the function you obtain satises the dierential equation. 6. (5 points) Bender & Orszag 3.24 (g) p.139. 7. (5 points) Bender & Orszag 3.24 (e) p.139. 8. (5 points) Bender & Orszag 3.24 (i) p.139....
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