Answer without code. Full steps and answers please.

Question $2(20pts)-$A reinforced concrete beam $(L=5m,E=30$GPa$)$ is subjected to a distributed

triangular load and a moment in the centre. The beam is supported, so you know that the displacement

at $x=0$ and $x=L$ is $0.$

The beam is of unusual shape, such that the moment of inertia varies with a function of $x$ with the

following equation:

$I(x)=I_0(1+\frac{x}{L})$

$I_0=2{10}^{9}m{m}^4$

Where $I_0$ is the moment of inertia when $x=0.$

The differential equation that allows us to get the deflection is as follows, and you get the equation for

the internal bending moment as a function of $x(M(x))$ :

$\frac{d^{2}y}{d{x}^2}=\frac{M(x)}{EI(x)}$

$M(x)=\frac{w_{\text{m}\text{a}\text{x}}}{3L^2}(L^{2}x-x^3)+M_0$

Find the solution of the differential equation $($deflection$)$ with:

The shooting method with a $x=0\mathrm{.}1m.$ Use Euler's method with the initial assumptions $(0)=0\mathrm{.}005$

and $(0)=-0\mathrm{.}005.$ Use linear interpolation to get the correct value of $(0)$ from both assumptions, given

that $y(L)=0.$ Then, plot the solution for the interpolated value of $(0).$