Question 1.Consider the first order equation:(sec2(y))y′−3 tan(y) + 12 = 0. This equation is not linear, clearly no algebraic manipulation can be done to put it in the standard linear form. However, by making a suitable substitution we actually can transform it.Using the substitution z= tan(y), rewrite this equation as a linear first order equation in standard form. Show your work. NOTE: The y′ notation hides something really important. You want to use the dy/dx style notation here. Question 2. Now solve that equation for z, and use the original substitution together with your solution to determine a solution for y. Show your work.
Question 1.Consider the first order equation:(sec2(y))y′−3 tan(y) + 12 = 0. This equation is not linear, clearly no algebraic manipulation can be done to put it in the standard linear form. However, by making a suitable substitution we actually can transform it.Using the substitution z= tan(y), rewrite this equation as a linear first order equation in standard form. Show your work. NOTE: The y′ notation hides something really important. You want to use the dy/dx style notation here. Question 2. Now solve that equation for z, and use the original substitution together with your solution to determine a solution for y. Show your work.
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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Question 1.Consider the first order equation:(sec2(y))y′−3 tan(y) + 12 = 0. This equation is not linear, clearly no algebraic manipulation can be done to put it in the standard linear form. However, by making a suitable substitution we actually can transform it.Using the substitution z= tan(y), rewrite this equation as a linear first order equation in standard form. Show your work. NOTE: The y′ notation hides something really important. You want to use the dy/dx style notation here.
Question 2. Now solve that equation for z, and use the original substitution together with your solution to determine a solution for y. Show your work.
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