you need to find in part (b) ... I would use the value of given in part (d)
You are correct on both counts. That is the correct differential equation for (a), and it looks like they want a numerical answer to (b) but to get that, you would need to know what Ts is.
For part (d), it looks like they want you to use the numerical value from (b).
I didn't see skeeter's post earlier. You can get a solution by using the Ts from part (d), but you don't know if that's what the author intended. There's a problem with the question either way.