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N 1. Solve each of the following initial value problems and plot the solutions for several values of yo. Then describe in a few words how the solutions resemble, and differ from, each other. a. dy/dt = -y +5, b. dy/dt = -2y +5, c. dy/dt = -2y + 10, y(0) = Yo y(0) = yo y(0) = yo

N 1. Solve each of the following initial value problems and plot the solutions for several values of yo. Then describe in a few words how the solutions resemble, and differ from, each other. a. dy/dt = -y +5, b. dy/dt = -2y +5, c. dy/dt = -2y + 10, y(0) = Yo y(0) = yo y(0) = yo

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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functions, many of them are associated with the names of mathematic (Section 5.7), Legendre (Section 5.3), Hermite (Section 5.2), Chebyshev and many others. Problems N 1. Solve each of the following initial value problems and plot the solutions for several values of yo. Then describe in a few words how the solutions resemble, and differ from, each other. a. dy/dt = -y +5, b. dy/dt = -2y +5, c. dy/dt = -2y + 10, G 2. Follow the instructions for Problem 1 for the following initial-value problems: - a. dy/dt = y = 5, y(0) = yo y(0) = yo y(0) = yo y(0) = yo G b. dy/dt = 2y = - c. dy/dt = 2y - 10, 3. Consider the differential equation 5, y(0) = Yo y(0) = yo dy/dt = -ay+b, where both a and b are positive numbers. a. Find the general solution of the differential equation. Gb. Sketch the solution for several different initial conditions. c. Describe how the solutions change under each of the following conditions: i. a increases. ii. b increases. iii. Both a and b increase, but the ratio b/a remains the same. 4. Consider the differential equation dy/dt = ay - b. a. Find the equilibrium solution ye. Y(t) is the deviation from the No CO car me or € d
Transcribed Image Text:functions, many of them are associated with the names of mathematic (Section 5.7), Legendre (Section 5.3), Hermite (Section 5.2), Chebyshev and many others. Problems N 1. Solve each of the following initial value problems and plot the solutions for several values of yo. Then describe in a few words how the solutions resemble, and differ from, each other. a. dy/dt = -y +5, b. dy/dt = -2y +5, c. dy/dt = -2y + 10, G 2. Follow the instructions for Problem 1 for the following initial-value problems: - a. dy/dt = y = 5, y(0) = yo y(0) = yo y(0) = yo y(0) = yo G b. dy/dt = 2y = - c. dy/dt = 2y - 10, 3. Consider the differential equation 5, y(0) = Yo y(0) = yo dy/dt = -ay+b, where both a and b are positive numbers. a. Find the general solution of the differential equation. Gb. Sketch the solution for several different initial conditions. c. Describe how the solutions change under each of the following conditions: i. a increases. ii. b increases. iii. Both a and b increase, but the ratio b/a remains the same. 4. Consider the differential equation dy/dt = ay - b. a. Find the equilibrium solution ye. Y(t) is the deviation from the No CO car me or € d
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