Just so we're clear, is this your equation?
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))