Express the following second-order differential equation as a pair of first-order equations:

Xy’’−y’−8x³y³ = 0

With the initial conditions y=1/2andy=−1/2atx=1.Solvethepairoffirst-orderequations using both ode23 and ode45 in the range 1 to 4. The exact solution is given by y=1/(1+x²). Use function fhermite to solve:

(a) Problem 5.1 with h=1.

(b) Problem 5.2 with h=0.2.

(c) Problem 5.2 with h=0.02

Use the MATLAB function rombergx to solve the following problems. In each case use eight divisions.

(a) y=3y/x with initial conditions x=1, y=1. Determine y when x=20.

(b) y=2xy with initial conditions x=0, y=2. Determine y when x=2