$(20)$ A vertical column of length $L,$ hinged at both ends, is subjected to a constant

compressive load $P,$ as shown in Fig $1$ below, is governed by

$EI{y}^{\text{'}\text{'}}+Py=0$;$,y(0)=y(L)=0$

where $E$ is the modulus of elasticity, and I is the moment of inertia. For what values of $P$ will

the column bend?

Fig $1.$ Column buckling under a compressive load