Differential Equations Lecture Work Solutions 253

Differential Equations Lecture Work Solutions 253 - e. The...

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Unformatted text preview: e. The set of ODEs is du =x dt dx =x dt The solution of the first is ln x = ln x0 + t or x = x0 et Now substitute x in the second ODE du = x0 et dt and integrate it u(x, t) = et x0 + K At t = 0 the solution is u(x0 , 0) = f (x0 ) = K + x0 plug t = 0 in the solution u Thus when substituting K in u u(x, t) = x0 et + f (x0 ) − x0 Now substitute for x0 in the solution u(x, t) = x + f x e−t − x e−t 253 ...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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