Differential Equations Lecture Work Solutions 171

Differential Equations Lecture Work Solutions 171 - 2. y +...

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2. y 0 + λ 2 y =0 0 <x< 2 π y (0) = y (2 π ) y 0 (0) = y 0 (2 π ) The eigenvalues λ n = n, n =0 , 1 , 2 ,... The eigenfunctions y n = cos nx sin nx 3. y 0 + y 0 +( λ +1) y =0 0 <x<π y (0) = y ( π )=0 Try y = e µx ,then µ 2 + µ + λ +1 = 0 The characteristic values µ are then µ = 1 ± ± 1 4( λ +1) 2 . Thereare3poss ib lecases . case 1: 1 4( λ +1) > 0, then we have two real µ . µ 1 = 1 2 + r, µ 2 = 1 2 r, where r = ± 1 4( λ +1) 2 . The solution is y ( x )= e x/ 2 ( Ae rx + Be rx
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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