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###### Problem 5. Let f be the function defined in the previous problem, so f(t) dr C...

Problem 5. Let f be the function defined in the previous problem, so f(t) dr C Show that the inverse of this function is a solution of the differential equation y+y 1. That is, let g(t) function g and its derivative. It says that the parametric curve y(t) the solution set of the equation g equation. This is one of a family of curves known as elliptic curves. The connection with ellipses f(t). Show that g(t)2-1-g(t)4. This is a kind of "Pythagorean identity" for this (g(t), g'(t)) has its image in 1-. Use Wolfram Alpha to graph the solution set of this is that these functions arise as inverses of are length functions for ellipses (as well as other curves with similar properties, like lemniscates) Problem 6, In the integral

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