I have 2 solutions off my teacher which is right??

0<= x <= 1 and t > 0

 <br />
u_x (0,t) = u_x (1,t) = 0<br />

for
0<= x <= 1 and t > 0

My one general solution has At + b before the series and the other doesn't which is right.

Im guessing its due to lambda = 0 but do we need it or not