Differential Equations Lecture Work Solutions 245

Differential Equations Lecture Work Solutions 245 - 7.2...

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7.2 Quasilinear Equations 7.2.1 The Case S =0 ,c = c ( u ) Problems 1. Solve the following a. ∂u ∂t = 0 subject to u ( x, 0) = g ( x ) b. = 3 xu subject to u ( x, 0) = g ( x ) 2. Solve = u subject to u ( x, t )=1+cos x along x +2 t 3. Let + c ∂x c = constant a. Solve the equation subject to u ( x, 0) = sin x b. If c> 0, determine u ( x, t )for x> 0and t> 0where u ( x, 0) = f ( x )f o r 0 u (0 ,t )= g ( t o r 0 4. Solve the following linear equations subject to u ( x, 0) = f ( x ) a. + c = e 3 x b. + t =5 c. t 2 = u d. + x = t e. + x =
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