Write an algorithm for predictor$-$corrector method to find the approximate solution of the IVP corresponding to a $1$st order linear ODE $)=f(t,y(t)),y(0)=(y_0.$ Write a MATLAB code to solve the following IVP by taking the step parameter $h=0\mathrm{.}1$ :

$y^{\text{'}}(t)+0\mathrm{.}2y(t)=0,y(0)=5in[0,1].$

Make a table and compare the approximate and exact solutions at node points. Demonstrate MATLAB code by plotting the approximate and exact solutions at the respective node points.