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(Solved): Consider the non-homogenous one-dimensional heat equation with non-homogeneous boundary conditions ...
Consider the non-homogenous one-dimensional heat equation with non-homogeneous boundary conditions \[ \begin{aligned} u_{t} &=u_{x x}-u, & & 00, \\ u_{x}(0, t) &=0, & & t>0, \\ u_{x}(a, t) &=T_{0}, & & t>0, \\ u(x, 0) &=\frac{T_{1} x}{a}, & & 00, \\ u_{x}(0, t) &=0, & & t>0, \\ u_{x}(a, t) &=0, & & t>0, \\ u(x, 0) &=f(x), & & 0