deletions | additions       diff --git a/The_equation_for_the_ellipsoid__.tex b/The_equation_for_the_ellipsoid__.tex  index 2d76553..6d52d59 100644  --- a/The_equation_for_the_ellipsoid__.tex  +++ b/The_equation_for_the_ellipsoid__.tex 
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We can formulate this as  $$x_k(t):=\frac{e_k^2}{t+e_k^2} y_k, \qquad k=1,2,3$$  and  $$x_k'(t) = -\frac{e_k^2}{(t+e_k^2)^2} y_k, y_k = -\frac{x_k(t)}{t+e_k^2},  \qquad k=1,2,3$$ We plug this into the expression for $E$,  $$E(t)=\frac{x_1^2(t)}{e_1^2} + \frac{x_2^2(t)}{e_2^2} + \frac{x_3^2(t)}{e_3^2} - 1$$  The derivative $E'(t)$: 
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