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
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