A beam is fixed on one end at $x=0.$ The boundary conditions at the other end are unknown and unimportant. Which of the following can we can conclude about the spatial expression of the solution?

$W(x)=C_{1}cosx+C_{2}sinx+C_{3}coshx+C_{4}sinhx$

a$)C_1=-C_3$ and $C_2=-C_4$

b$)C_1=C_2$ and $C_3=-C_4$

c$)C_1=C_3$ and $C_2=-C_4$

d$)C_1=C_3$ and $C_2=C_4$

e$)C_1=0$ and $C_3=0$