Brewer_MAT_275_ONLINE_B_Spring_2018.digamble.MAT_275_TEST_1,v1.pdf

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David Gamble Brewer MAT 275 ONLINE B Spring 2018 Assignment MAT 275 TEST 1 due 03/30/2018 at 11:39pm MST Problem 1. 1. (1 point) A function y ( t ) satisfies the differ- ential equation dy dt = - y 4 - 3 y 3 + 40 y 2 . (a) What are the constant solutions of this equation?
(b) For what values of y is y increasing?
Answer(s) submitted: 0,-8,5 -8 5 (correct) Problem 2. 2. (1 point) It can be helpful to classify a differ- ential equation, so that we can predict the techniques that might
help us to find a function which solves the equation. Two clas- sifications are the order of the equation – (what is the highest number of derivatives involved) and whether or not the equation is linear . Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear: ? 1. d 2 y dt 2 + sin ( t + y ) = sin t ? 2. y 00 - y + t 2 = 0

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