Solve the 1-Dimensional heat equation for the conduction of heat along the rod without radiation with conditions:i) u(x,t) is finite for t tends to infiniteii) ux(0,t) = 0 and ux(l,t) = 0iii) u(x,t) = x(l-x) for t=0 between x=0 and x=l.

• A. U(x,t) =\(\frac{l^2}{3}/2 + ∑cos⁡(\frac{nπx}{l}) e^{\frac{-c^2 n^2 π^2 t}{l^2}} \frac{-4l^2}{(2m)^2+π^2} \)
• B. U(x,t) =\(\frac{l^2}{3} + ∑cos⁡(\frac{nπx}{l}) e^{\frac{-c^2 n^2 π^2 t}{l^2}} \frac{-4l^2}{(2m)^2+π^2} \)
• C. U(x,t) =\(\frac{l^2}{3} + ∑cos⁡(\frac{nπx}{l}) e^{\frac{-c^2 n^2 π^2 t}{l^2}} \frac{4l^2}{(2m)^2+π^2} \)
• D. U(x,t) =\(\frac{l^2}{3}/2 + ∑cos⁡(\frac{nπx}{l}) e^{\frac{-c^2 n^2 π^2 t}{l^2}} \frac{4l^2}{(2m)^2+π^2} \)