Differential Equations: An Introduction to Modern Methods and Applications

3rd Edition

ISBN: 9781118531778

Author: James R. Brannan, William E. Boyce

Publisher: WILEY

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Textbook Question

Chapter 1.2, Problem 2P

Phase Line Diagrams. Problems 1 through 7 involve equation of the form d y / d t = f ( y ) . In each problem, sketch the graph of f ( y ) versus y , determine the critical (equilibrium) points, and classify each one as asymptotically stable or unstable. Draw the phase line, and sketch several graphs of solutions in the t y − plane.

d y / d t = e y − 1 , − ∞ < y 0 < ∞ .

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Chapter 1.2, Problem 1P

Chapter 1.2, Problem 3P

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2a. Find a change of variable that transforms the equation into an autonomous equation change of variable: new equation: b. Sketch the phase line for the resulting equation and use it to sketch graphs of the long-term behaviors of all the qualitatively different solutions for the new variable, and then for the original equation.

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In each question, draw the phase diagram (i.e. the graph with stationary points and arrows), determine the stationary points, and classify each one as stable, unstable or seminstable (by considering the sign of the derivative of the right-hand side). 1. i = -x + 1 2. i = 2x – x² 3. i = -x(1+x)(2 – x) 4. i = x? – x4 5. i = x²(4 – x²)

Chapter 1 Solutions

Differential Equations: An Introduction to Modern Methods and Applications

Ch. 1.1 - Newton’s Law of Cooling. A cup of hot coffee has...Ch. 1.1 - Blood plasma is stored at . Before it can be...Ch. 1.1 - At 11:09p.m. a forensics expert arrives at a crime...Ch. 1.1 - The rate constant if the population doubles in ...Ch. 1.1 - The field mouse population in Example 3 satisfies...Ch. 1.1 - Radioactive Decay. Experiments show that a...Ch. 1.1 - A radioactive material, such as the isotope...Ch. 1.1 - Classical Mechanics. The differential equation for...Ch. 1.1 - For small, slowly falling objects, the assumption...Ch. 1.1 - Mixing Problems. Many physical systems can be cast...

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