Question $1$

The boundary condition at $x=0$ is:

$u(0)=0$

$P(0)=0$

$u_x(0)=\frac{p_{o}L}{AE}$

$P(0)=p_{o}L$

$P(0)=-p_{o}L$

$u_x(0)=-\frac{p_{o}L}{AE}$

Question $2$

The boundary condition at $x=L$ is:

$u_x(L)=-\frac{p_{o}L}{AE}$

$u(L)=0$

$P(L)=-p_{o}L$

$P(L)=p_{o}L$

$P(L)=0$

$u_x(L)=\frac{p_{o}L}{AE}$