Solve the boundary$-$value problem

$y^{\text{'}\text{'}}+x^2{y}^{\text{'}}-4xy=2x^3+6x^2-2,y(0)=0,y(1)=2$

by using the shooting method. Use the modified Euler method $($with only one correction at each step$),$ and take $h=0\mathrm{.}2.$ Start with an initial slope of $y^{\text{'}}(0)=1\mathrm{.}9$ as a first attempt a nd $y^{\text{'}}(0)=2\mathrm{.}1$ as a second attempt. Then interpolate using MATLAB code and provide a complete MATLAB you used $,$ your output program must show tabular interpolation.

Compare the result with the analytical solution $y=x^4-x^2+2x.$