find the solution of the given initial value problem. Sketch the graph of the solution and describe its behavior as t increases. y″ + y′ − 2y = 0, y(0) = 1, y′(0) = 1 6y″ − 5y′ + y = 0, y(0) = 4, y′(0) = 0 4y″ − y = 0, y(−2) = 1, y′(−2) = −1

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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find the solution of the given initial value problem. Sketch the graph of the solution and describe its behavior as t increases.

y″ + y′ − 2y = 0, y(0) = 1, y′(0) = 1

6y″ − 5y′ + y = 0, y(0) = 4, y′(0) = 0

4y″ − y = 0, y(−2) = 1, y′(−2) = −1

 

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