1. Solve the Heat problem
uₜ (x,t) = k(uₓₓ(x,t) - 2auₓ(x,t) + bu(x,t)), 0 < x < l, t > 0
u(0,t) = 0, u(l,t) = 0 and u(x,0) = f(x)
Hint: Use substitution
u(x,t) = eᵃˣ⁺βᵗ v(x,t), β = k(b - a²)
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