there is the equation x'' x(2x^2 1) = 0 with initial conditions x(0) = 1, x'(0) = 0.

(a) Write as a system of first order equations in the standard way.

(b)What does Theorem 7.1.1 say about existence and uniqueness of solutions?

(c)prove that x = sec(t) is a solution by confirming that it satisfies the differential equation and initial condition.

(d) what is the maximal interval on which a unique solution actually exists.

Theorem 7.1.1 Let each of the functions F1.....F, and the partial derivatives aF/ax,.... aF1/2X.,...,aF,/ax1,..., aF,/ax, be continuous in a region R of tug .. .X- space defined by a