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Differential Equations Lecture Work Solutions 237

Differential Equations Lecture Work Solutions 237 - dx dt =...

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4. The ODEs in this case are dx dt = 2 u du dt = 0 with u ( x, 0) = f ( x ) = 1 x < 0 1 + x L 0 < x < L 2 L < x a. Since the first ODE contains x , t and u , we solve the second ODE first u ( x, t ) = u ( x (0) , 0) = f ( x (0)) Plug this u in the first ODE, we get
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Unformatted text preview: dx dt = 2 f ( x (0)) The solution is x = x + 2 tf ( x )-5 5 10 15 20 25 0.5 1 1.5 2 2.5 3 3.5 4 x t Figure 46: Characteristics ±or problem 4 237...
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