The boundary value problem $y^{\text{'}\text{'}}(x)+y^{\text{'}}(x)=xy(x),y(0)=1,y^{\text{'}}(3)=2$ is

discretized using central differences with step $h=1.$ Give the coordinate of the

fictitious grid point $x=$

$($enter integer value$).$ Determine the values

of the solution at $x=1,x=2$ and $x=3$:$y(1)=$

$,y(2)=$

$y(3)=$

$.$ Round the answer to the fourth

decimal place. $($Hint: You may proceed as in Q$2$ and Q$3$ of tutorial $7.$ Also note

that by default, Matlab rounds the answer to the fourth decimal place$).$

Now use the for loop to write a Matlab code that solves the above boundary value

problem for the arbitrary discretization step $h.$ Use $h=0\mathrm{.}1$ to determine the solution

at $x=3$:$y(3)=$

$($Round the answer to the fourth decimal

place$).$