= 1. (20 pts) Find a series solution for the following boundary-value problem, Um + Uy 0, 0
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= 1. (20 pts) Find a series solution for the following boundary-value problem, Um + Uy 0, 0
= 1. (20 pts) Find a series solution for the following boundary-value problem, Um + Uy 0, 0<x<1, 0<y <1, ux(0,y) 1, 0<y <1, tu(1, ) 0, 0<y <1, u(3,0) 0, 0<x<1, u(3,1) 2, 0 <3 <1, using the method of separation of variables. (Note that you need to find an auxiliary function so that one set of boundary conditions are zero after substitution.)
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