Differential Equations Lecture Work Solutions 136

Differential Equations Lecture Work Solutions 136 - u t = u...

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5.2 Method of Eigenfunction Expansions Problems 1. Solve the heat equation u t = ku xx + x, 0 <x<L subject to the initial condition u ( x, 0) = x ( L x ) and each of the boundary conditions a. u x (0 ,t )=1 , u ( L, t )= t. b. u (0 ,t )=1 , u x ( L, t )=1 . c. u x (0 ,t )= t, u x ( L, t )= t 2 . 2. Solve the heat equation
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Unformatted text preview: u t = u xx + e t , &lt; x &lt; , t &gt; , subject to the initial condition u ( x, 0) = cos 2 x, &lt; x &lt; , and the boundary condition u x (0 , t ) = u x ( , t ) = 0 . 136...
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