Write a Matlab program which solves the initial value problem

y

 = (xy − y2)/x2, y(1) = 2,

by the order four Runge-Kutta method, over the interval [1, 3] using steps of h = 1/128. The exact solution to

this problem is given by y(x) = x/(ln x + 1/2).

Your program should display a plot of the Runge-Kutta solution and the exact solution on the same axes

and should print out the norm of the relative error of the numerical solution. Be sure to label the x,y axes of

the plot and to put a title on the plot.-Write a Matlab program which solves the initial value problem

y

 = (xy −　y2)/x2, y(1) = 2,

by the order four Runge-Kutta method, over the interval [1, 3] using steps of h = 1/128. The exact solution to

this problem is given by y(x) = x/(ln x+ 1/2).

Your program should display a plot of the Runge-Kutta solution and the exact solution on the same axes

and should print out the norm of the relative error of the numerical solution. Be sure to label the x,y axes of

the plot and to put a title on the plot.