okay so i was giving this question i know its 2nd order differential equations but im not sure how to approach it if some one could help i would be thankful

Question:

A column of length L is subjected to a compressive load P.

The displacement, y, at a distance x is given by the solution of EI d^{2}y/dx^{2}+Py=0

(i) Show that y = Acos (kx) + Bsin(kx), where k=√P/EI

(ii) The critical load is the value of the load P, that will cause buckling. This critical load,

P

CR

, occurs for the boundary conditions x = 0, y = 0, and x = L, y = 0. Show that the

critical load is given by:

where n is any whole number

(Note that Sin (np) = 0, where n is any whole number).