Differential Equations Lecture Work Solutions 280

Differential Equations Lecture Work Solutions 280 - 7.3.2...

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7.3.2 Semi-infnite String 7.3.3 Semi-infnite String with a Free End Problems 1. Solve by the method of characteristics 2 u ∂t 2 c 2 2 u ∂x 2 =0 ,x > 0 subject to u ( x, 0) = 0 , ∂u ( x, 0) = 0 , u (0 ,t )= h ( t ) . 2. Solve 2 u 2 c 2 2 u 2 < 0 subject to u ( x, 0) = sin x, x < 0 ( x, 0) = 0 < 0 u (0 e t > 0 . 3. a. Solve 2 u 2 c 2 2 u 2 , 0 <x< subject to u ( x, 0) = 00 2 12 3 03 <x ( x, 0) = 0 , (0 )=0 . b. Suppose u is continuous at
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