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) =B_{0} /2 + (a sum). Then u(1,θ) = A_{0} /2 + (a sum). I'm not sure how B_{0} turned into A_{0} in this.

Thank you!