the temperature T of a cooling fan of finite length, L satisfies

d2T/dx2=-K^2*(T(sub L)-T) 0<=x<=L T(0)=T0 T(L)=T(sub L) TL

where K, T0 and TL are constant

a) find the complimentary function Tc(x) stating your answer in terms of unknown constants c1 and c2

answer for this part is: Tc(x)=c1cosh(xk)+c2sinh(xK)

b) complete the following

sinh(KL-Kx)=

answer for it is: =[sin(kL)cos(KL)-cos(kL)sin(kx)]

now this is where i have problems

c) write down your starting point for the particular solution Tp(x)

d) find Tp(x) and the coefficients c1, and c2 and hence show that the solution of the above problem is

T(x)=Tl+(T0-TL)(sing(k(L-x))/sinh(KL))