Question: Solve the following PDEs with Boundary conditions using separable Method (b) Suppose we wish to find the steady-state temperature u(x,y) in a regular plate whose

Solve the following PDEs with Boundary conditions using separable Method

(a) du du x t u(0, t) = 0, u(L, t) = 0, t> 0 a- = u(x, 0) = f(x), 0

(b) Suppose we wish to find the steady-state temperature u(x,y) in a regular plate whose vertical edges x=0 and x=a are insulated. when no heat escapes from the lateral faces of the plate, we solve the following boundary-value problem

du du + dx dy 0, 0, xlx=0 xlx=a u(x, 0) = 0, u(x, b) = f(x), 0

(a) du du x t u(0, t) = 0, u(L, t) = 0, t> 0 a- = u(x, 0) = f(x), 0

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