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Find the generalized Fourier series solution to the homogeneous Robin problem for the heat equation u (7(x)) - B(x)u, 0 < x < 1,

 

Find the generalized Fourier series solution to the homogeneous Robin problem for the heat equation u (7(x)) - B(x)u, 0 < x < 1, t>0, a(z) 4-0 (7(2) 4) t = == au(0, t) B1 (0,t) = 0, t> 0, x Ju aqu(l, t) + B2- (l,t) = 0, t> 0, dx u(x, 0) = f(x), 0 < x 0, 7(x) > 0, and (x) > 0 for 0 < x < l.

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