Explanation Given: The differential equation is d y d x = y e y − 9 y e y . Calculation: Consider the given differential equation. d y d x = y e y − 9 y e y (1) Write the equation of equilibrium and solve for variable y . Substitute 0 for d y d x in equation(1) and solve to find the critical points. y e y − 9 y e y = 0 y e y − 9 y = 0 y ( e y − 9 ) = 0 Further solve for factor y = 0 . y = 0 And for factor ( e y − 9 ) = 0 . ( e y − 9 ) = 0 e y = 9 ln 9 = y Therefore, the critical points are 0 and ln 9 , And equilibrium equations are y ( x ) = 0 and y ( x ) = ln 9 . Take the critical points as 0 and ln 9 on a vertical line and then defined it into three intervals, as follows; − ∞ < y < 0 , 0 < y < ln 9 and ln 9 < y < ∞ . Write the differential equation in terms of f ( y ) as follows. f ( y ) = y ( e y − 9 ) e y (2) To find the algebraic sign take the points on the constructed intervals and substitute it in equation (2) as below, For interval − ∞ < y < 0 substitute − 1 for y in equation(2). f ( − 1 ) = ( − 1 ) ( e − 1 − 9 ) e − 1 = − e − 1 e − 1 + 9 e − 1 = 9 e − 1 Therefore, for interval − ∞ < y < 0 the algebraic sign is positive

Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th

11th Edition

ISBN: 9781305965737

Author: Dennis G. Zill

Publisher: Brooks Cole

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Chapter 2.1, Problem 28E

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To sketch: The typical solution curve in the region in the xy-plane determined by the graph of equilibrium solutions.

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Chapter 2.1, Problem 27E

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Student Solutions Manual For Zill's A First Course In Differential Equations With Modeling Applications, 11th

Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - dydx=1xy (a) y(0) = 0 (b) y(1) = 0 (c) y(2) = 2...Ch. 2.1 - In Problems 14 reproduce the given...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...Ch. 2.1 - In Problems 512 use computer software to obtain a...

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The typical solution curve in the region in the x y -plane determined by the graph of equilibrium solutions.

Solution Summary: The author illustrates the typical solution curve in the xy -plane determined by the graph of equilibrium solutions.

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To sketch: The typical solution curve in the region in the xy-plane determined by the graph of equilibrium solutions.

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