Unformatted text preview: y 00xy + 2 y = 0 about the x = 0 . 8. The function f ( x ) = 1 + (1 / 2) x on the interval 0 ≤ x ≤ 2 . Find the Fourier sine series of this function. 9. Let A = ± 2 1 0 2 ¶ . Solve x = A x , x (0) = ± 2 5 ¶ . 10. Determine whether x = 0 is a regular singular point of x 3 y 00 + 2 x 2 y + y = 0 . 11. (Ultramegabonus) Solve the following BVP involving the wave equation, where u ( x,t ) is the position of a string with ﬁxed ends at time t . 4 u xx = u tt ,u (0 ,t ) = 0 = u (6 ,t ) ,u ( x, 0) = f ( x ), where f ( x ) = x on the interval 0 ≤ x ≤ 6....
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 Spring '08
 Fonken
 Differential Equations, Equations, ORDINARY DIFFERENTIAL EQUATIONS, Partial differential equation, general solution, BVP, Fourier sine series, M427K Final Exam

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