Problem $5\mathrm{.}11.$ Cantilever beam with tip spring

Consider the cantilevered beam of length L with a tip spring of stiffness k depicted in fig. $5\mathrm{.}38.$

The beam is subjected to a uniform transverse load, p$\_(0),$ and a tip concentrated load, P$.(1)$

Write the governing differential equation and associated boundary conditions for this problem.

Fig. $5\mathrm{.}38.$ Cantilevered beam with tip spring.