Differential Equations Lecture Work Solutions 247

Differential Equations Lecture Work Solutions 247 - 1. a....

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Unformatted text preview: 1. a. Integrate the PDE assuming x fixed, we get u(x, t) = K (x) Since dx/dt = 0 we have x = x0 and thus u(x, t) = u(x0 , 0) = K (x0 ) = g (x0 ) = g (x) u(x, t) = g (x) b. For a fixed x, we can integrate the PDE with respect to t du = − 3xt + K (x) u ln u − ln c(x) = − 3xt u(x, t) = ce−3xt Using the initial condition u(x, t) = f (x) e−3xt 247 ...
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