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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781285740621

Chapter 17.2, Problem 18E

Textbook Problem

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Write a trial solution for the method of undetermined coefficients. Do not determine the coefficients.

To determine

**To write:**

A trial solution for the method of the undetermined coefficients.

**1) Concept:**

**i) General solution of **

Roots of |
General solution |

**ii) undetermined coefficients method:**

i) If

ii) If

iii) If any term of

**2) Given:**

**3) Calculations:**

Consider the given differential equation

The auxiliary equation of the homogeneous differential equation is

Solving the auxiliary equation

Therefore, by concept (i) the complementary solution is

Let

Letting

Where

By using the concept ii),

The trial solution of the form

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Ch. 17.1 - Solve the differential equation. yy6y=0Ch. 17.1 - Solve the differential equation. y6y+9y=0Ch. 17.1 - Solve the differential equation. y+2y=0Ch. 17.1 - Solve the differential equation. y+y12y=0Ch. 17.1 - Solve the differential equation. 4y+4y+y=0Ch. 17.1 - Solve the differential equation. 9y+4y=0Ch. 17.1 - Solve the differential equation. 3y=4yCh. 17.1 - Solve the differential equation. y=yCh. 17.1 - Solve the differential equation. y4y+13y=0Ch. 17.1 - Solve the differential equation. 3y+4y3y=0

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A spring with an 8-kg mass is kept stretched 0.4 m...Ch. 17.3 - A spring with a mass of 2 kg has damping constant...Ch. 17.3 - A force of 13 N is needed to keep a spring with a...Ch. 17.3 - For the spring in Exercise 3, find the mass that...Ch. 17.3 - For the spring in Exercise 4, find the damping...Ch. 17.3 - A spring has a mass of 1 kg and its spring...Ch. 17.3 - A spring has a mass of 1 kg and its damping...Ch. 17.3 - Suppose a spring has mass m and spring constant k...Ch. 17.3 - As in Exercise 9, consider a spring with mass m,...Ch. 17.3 - Show that if 0, but /0 is a rational number, then...Ch. 17.3 - Consider a spring subject to a frictional or...Ch. 17.3 - A series circuit consists of a resistor with R=20,...Ch. 17.3 - A series circuit contains a resistor with R=24 an...Ch. 17.3 - The battery in Exercise 13 is replaced by a...Ch. 17.3 - The battery in Exercise 14 is replaced by a...Ch. 17.3 - Verify that the solution to Equation 1 can be...Ch. 17.3 - The figure shows a pendulum with length L and the...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - The solution of the initial-value problem...Ch. 17.R - a Write the general form of a second-order...Ch. 17.R - a What is an initial-value problem for a...Ch. 17.R - Write the general form of a second-order...Ch. 17.R - Discuss two applications of second-order linear...Ch. 17.R - How do you use power series to solve a...Ch. 17.R - Determine whether the statement is true or false....Ch. 17.R - 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