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Question: hw assignment 1due 1000 am january 29 tuesday a...

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HW Assignment 1-due 10:00 AM, January 29 (Tuesday) () A few problems will be selected and graded. Completion points will be given for the remaining problems. 1. Consider the differential equation dr for unknown function y(x) a) What is the order of the differential equation (t)? b) Let y(x) be a solution of the differential equation (t). Prove that y(x) is an increasing function. (Hint: You dont need to solve the differential equation to do this problem. An answer can be written in one sentence without computation.) 2. Classify the following differential equations as either . 1st order linear homogeneuous . 1st order linear nonhomogeneous or 1st order non-linear Explain briefly why your answer is correct for each case a) For unknown function f(r) f(x) f(x)2 0 b) For unknown function y(x) c) For unknown function y(r) ey (sin )y sin(2) d) For unknown function r(t) dr dt e cos t e) For unknown function y(r) sin(y+).yn(y2 +1) 3. Show that y(zsin z is a solution of the differential equation d2 dr2

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