On the Stability of Rod with Variable Cross-section

There is a solution of the problem of the stability of a compressed rod with a variable cross-section. A rectangular cross-section with a variable width is selected as the section. The result is that the problem leads to a differential equation of the fourth order with variable coefficients. From the solution of this equation, a critical force for several particular cases. These cases reflect some different conditions fixing rod and function changes of the width of the cross-section.