Chapter 4.4, Problem 47E

The figure shows a beam of length L embedded in concrete walls. If a constant load W is distributed evenly along its length, the beam takes the shape of the deflection curve

$y=\frac{W}{24EI}{x}^4+\frac{WL}{12EI}{x}^3-\frac{W{L}^2}{24EI}{x}^2$

where E and I are positive constants. (E is Young’s modulus of elasticity and I is the moment of inertia of a cross-section of the beam.) Sketch the graph of the deflection curve.