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Question: w help d map2302hw3pdf page 3 of 3 3 consider...

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w Help D MAP2302HW3.pdf (page 3 of 3) (3) Consider the initial value problem drv)( 2 (a) Rewrite the ODE in this IVP in the standard form of a Bernoulli equa- tion and then solve this IVP via the method described in Lecture 2.1 (cf. 2.3.B in the text). (b) Observe that this ODE is manifestly separable. Solve this IVP using the general method for solving separable ODE described in Lecture 2.2 / Section 2.2. Youll have to integrate a rational function using the method of Partial Fractions. (You havent forgotten how to do that, have you? Show me you havent... dont skip this step!) Make sure you get the same answer as in the previous part! (c) Observe that the solution y y(x) to this IVP is a strictly increasing differentiable function satisfying limo y(x) = 0 and lino y(x) = 1. -+00 The function y(x) is therefore the cumulative distribution function (CDF) for a continuous probability distribution. Do you know what this dis- tribution is called?
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