Explanation Given: The given electrical network is shown below. Figure (1) Calculation: Apply Kirchhoff’s first law. i 1 = i 2 + i 3 Apply Kirchhoff’s second law for each loop. E ( t ) = i 1 R 1 + L 1 d i 2 d t + i 2 R 2 (1) E ( t ) = i 1 R 1 + L 3 d i 3 d t + i 3 R 3 (2) Substitute i 2 + i 3 for i 1 in above equations. E ( t ) = ( i 2 + i 3 ) R 1 + L 1 d i 2 d t + i 2 R 2 = L 1 d i 2 d t + ( R 1 + R 2 ) i 2 + R 1</

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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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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Chapter 2.9, Problem 15E

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The system of first-order differential equations that describes the currents i2(t) and i3(t)

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Chapter 2.9, Problem 14E

Chapter 2.9, Problem 16E

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2. Consider the ODE u' = ƒ (u) = u² + r where r is a parameter that can take the values r = −1, −0.5, -0.1, 0.1. For each value of r: (a) Sketch ƒ(u) = u² + r and determine the equilibrium points. (b) Draw the phase line. (d) Determine the stability of the equilibrium points. (d) Plot the direction field and some sample solutions,i.e., u(t) (e) Describe how location of the equilibrium points and their stability change as you increase the parameter r. (f) Using the matlab program phaseline.m generate a solution for each value of r and the initial condition u(0) = 0.9. Print and turn in your result for r = −1. Do not forget to add a figure caption. (g) In the matlab program phaseline.m set the initial condition to u(0) = 1.1 and simulate the ode over the time interval t = [0, 10] for different values of r. What happens? Why? You do not need to turn in a plot for (g), just describe what happens.

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Advanced Engineering Mathematics

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The system of first-order differential equations that describes the currents i 2 ( t ) and i 3 ( t )

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Chapter 2 Solutions