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Differential Equations Lecture Work Solutions 253

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

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e. The set of ODEs is dx dt = x du dt = x The solution of the first is ln x = ln x 0 + t or x = x 0 e t Now substitute x in the second ODE du dt = x 0 e t and integrate it u ( x, t ) = e t x 0 + K At t = 0 the solution is u ( x 0 , 0) = f ( x 0 ) = K + x 0 plug t = 0 in the solution u Thus when substituting
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