1. The problem statement, all variables and given/known data Problem 29. Use the subtraction trick U(tilda) = U−U1 to reduce the following problems with non-canonical boundary conditions to the canonical ones and write down the equations in terms of the variable ˜u (do not solve them). Note that there are infinitely many u1’s that solve each problem—try to find the simplest ones. (a) Heat equation ut = Uxx , x ∈ [0, l] , with the following boundary conditions (a.1) u(0, t) = U(l, t) = A , (a.2) Ux(0, t) = 0 , U(l, t) = A , (a.3) U(0, t) = A , U(l, t) = B , (a.4) Ux(0, t) = Ux(l, t) = A , (a.5) Ux(0, t) = A , Ux(l, t) = B . (b) Wave equation with dissipation and a perturbation on one end Utt + aUt = c 2Uxx , x ∈ [0, l] 2. Relevant equations 3. The attempt at a solution I am using U1(x,t)= a(t)+(x-c).b(t) then U(x,t)=U(tilda)(x,t)+U1(x,t) I can find the U1's but not U(tilda) is that enough to transform them into canonical form? I'm googling like a mad man but no luck so far. can't find any good sources. you don't have to answer the question but a little help would be nice.