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Asymptotics [4pt] Consider the differential equation y" (x) a x y(x) = 0, where a > 0 is a constant. Show that a rescaling of x can eliminate a from the equa- tion. Using asymptotic methods, find the leading behaviour of the two solutions of the equation as x + too. You should find y(x) ~ F(x)(1+...), where the ... terms vanish as x + too, and F(x) either increases or decreases very fast as x + too. Find F(x) and the leading term in the ... for both solutions. Asymptotics [4pt] Consider the differential equation y" (x) a x y(x) = 0, where a > 0 is a constant. Show that a rescaling of x can eliminate a from the equa- tion. Using asymptotic methods, find the leading behaviour of the two solutions of the equation as x + too. You should find y(x) ~ F(x)(1+...), where the ... terms vanish as x + too, and F(x) either increases or decreases very fast as x + too. Find F(x) and the leading term in the ... for both solutions