I need help with this matlab problem. Thank you in advance.

Consider the following ODE:

$\frac{d^{2}y}{d{x}^2}+x^2\frac{dy}{dx}+y=4cos(x),$ for $,0x10,$ with $,y(0)=3,$ and $,y(10)=2$

Write a script that:

named ys$.$

finite difference approximations in your formulation.

b$)$ Solve for $y(x)$ using the finite difference method with $x=0\mathrm{.}5.$ Save result as a column vector named $ydx.$

c$)$ Solve for $y(x)$ using the finite difference method with $x=0\mathrm{.}25.$ Save result as a column vector named $ydx2.$

d$)$ Solve for $y(x)$ using the finite difference method with $x=0\mathrm{.}05.$ Save result as a column vector named $ydx3.$

e$)$ Compare the accuracy of your results for $($b$),($c$),$ and $($d$)$ by doing the following:

vectors of $lo{n}_a$ values. Note this means you will need to extract only the relevant $y$ values $($corresponding to the specified nodes$)$ from your solutions for $($b$),($c$)$ and $($d$)$ to use in this calculation.