Use RK$4-$Kutta Method

$(10$ points$)$

Example $9\mathrm{.}9.$ Solve

$\frac{d^{2}y}{d{x}^2}=\frac{M}{EI}=\frac{30x-1\mathrm{.}5x^2}{EI}$

where $EI=121,500$kips$-f{t}^2.$

The boundary conditions prescribed are

$y(0)=0$ and $y(20)=0.$

This differential equation represents the relationship between the bending moment $M$ and the deflection $y$ at a distance $x$ along the span from the left hand end of a $20$ foot long simply supported beam loaded with a uniformly distributed load of $3$kip$\frac{s}{f}t.$ as shown in Figure $9\mathrm{.}17.$ The slope and deflection at any point $x$ can be obtained by solving the above differential equation.

Fig. $9\mathrm{.}17$: A simply supported beam with a uniformly distributed load

Use Shooting method with step size $(h)=0\mathrm{.}5ft$

Need to solve using excel VBA

$(20$ points$)$