2022 midterm 2 solution: Possible typos?

[ravanasa]

I've been looking through the midterm solutions from 2022 to study for the midterm coming up. I was wondering if it's possible there are typos in the solutions, or if you can explain the following if I am misunderstanding something:

1. In problem 1 of Main Sitting 2022, there is the equation T' + 4λT = 0. I believe this should be T'' + 4λT = 0, with the first T as a second derivative.

2. In problem 1 of Morning Sitting 2022, there is equation 4T'' + λT = 0. I believe this should be T'' + 9λT = 0.
In the same question, T_n = A_n cos(nt) + B_n sin(nt). I believe this should be T_n = A_n cos(3nt) + B_n sin(3nt).
In the same question, there are initial boundary conditions dependent on the value of t. I believe in the solution when plugging these in, they are swapped.

3. In problem 3 of Main Sitting 2022, there u(r,θ) =B₀ /2 + (a sum). Then u(1,θ) = A₀ /2 + (a sum). I'm not sure how B₀ turned into A₀ in this.

Thank you!

[Victor Ivrii]

Thanks! Fixed