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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. ∂u ∂t = 3 xu subject to u ( x, 0) = g ( x ) 2. Solve ∂u ∂t = u subject to u ( x, t ) = 1 + cos x along x + 2 t = 0 3. Let ∂u ∂t + c ∂u ∂x = 0 c = constant a. Solve the equation subject to u ( x, 0) = sin x b. If c > 0, determine u ( x, t ) for x > 0 and t > 0 where u ( x, 0) = f ( x ) for x > 0 u (0 , t ) = g ( t ) for t > 0 4. Solve the following linear equations subject to u ( x, 0) = f (
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