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Differential Equations Lecture Work Solutions 236

Differential Equations Lecture Work Solutions 236 - 3 The...

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3. The ODEs in this case are dx dt = 2 u du dt = 0 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 dx dt = 2 f ( x (0)) The solution is x = x 0 + 2 tf ( x 0 ) These are characteristics lines all with slope
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