This is the question, I have solved it but I need someone to double check my solution. Question: Find the temperature $u(x, t)$ in a rod of length $L$ if the initial temperature is $f (x)$ throughout and if the ends $x=0$ and $x=L$ are insulated. $F(x) = \begin{cases} x, \ 0
Solution: For an insulated rod the solution $X(x,t)= a_0/2+\sum B_n cos(n\pi x/L)e^{(n^2π^2α^2)t/L}$
I found $a_0= 1$ and $Bn= (−(2/nπ)sin(nπ/2)+(2/nπ)2cos(nπ/2)−(2/nπ)^2)$
then just plug in the coefficients into the sum. I am just not sure if these are the correct values for the $a_0$ and $B_0$ coefficients.