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1. Solve the following differential equations. dy a) = (y - 1)(y + 2) dx

1. Solve the following differential equations. dy a) = (y - 1)(y + 2) dx

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Solve the following differential equations. dy a) dx dy b) dx c) y' d) y' = y² - 2y = = = (y − 1)(y + 2) sin x y
Transcribed Image Text:1. Solve the following differential equations. dy a) dx dy b) dx c) y' d) y' = y² - 2y = = = (y − 1)(y + 2) sin x y
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2. Skydiving If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of velocity, then the body's velocity t seconds into the fall satisfies the equation dv mmg - kv², k > 0 dt where k is a constant that depends on the body's aerodynamic properties and the density of the air. (We assume that the fall is too short to be affected by changes in the air's density.) Find the velocity of an object with a mass of 10 kg and a value of k = 0.05 N.s/m after: a) 10 s b) 100 s c) 1000 s
Transcribed Image Text:2. Skydiving If a body of mass m falling from rest under the action of gravity encounters an air resistance proportional to the square of velocity, then the body's velocity t seconds into the fall satisfies the equation dv mmg - kv², k > 0 dt where k is a constant that depends on the body's aerodynamic properties and the density of the air. (We assume that the fall is too short to be affected by changes in the air's density.) Find the velocity of an object with a mass of 10 kg and a value of k = 0.05 N.s/m after: a) 10 s b) 100 s c) 1000 s
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Solve B,C,D

1. Solve the following differential equations. dy a) dx dy b) dx y c) y' √y d) y' = y² - 2y gladinin T = = = (y - 1)(y + 2) sin x S
Transcribed Image Text:1. Solve the following differential equations. dy a) dx dy b) dx y c) y' √y d) y' = y² - 2y gladinin T = = = (y - 1)(y + 2) sin x S
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