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l OlI SAne coordinate axes for >0 2. Show that the function φ(z) = (2-22)-1 is a solution to the initial value problem, dy/dr 2xy, y(0) 1/ on the interval -cc. Graph the solution curves corresponding toc = 1/2. 1 and 2, on the same axes. (Aside: This solution becomes unbounded as r approaches tc. Thus, the solution exists on ( -8, δ) with δ c but not for larger δ. This shows that the interval of existence of a solution can be quite small (if c is small) or large (if c is large) Notice there is no clue from the differential equation itself dy/dr 2xy2, or from the initial value, that the solution will blow up at -tc. This is a nonlinear problem.)

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