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Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621
BuyFind

Calculus (MindTap Course List)

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781285740621

Solutions

Chapter
Section
Chapter 17.2, Problem 15E
Textbook Problem

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

y 3 y + 2 y = e x + sin x

Expert Solution
To determine

To write:

A trial solution for the method of the undetermined coefficients.

Explanation of Solution

1) Concept:

i) General solution of ay''+by'+cy=0:

Roots of ar2+br+c=0 General solution 
r1, r2  are real and distinct y=c1er1x+c2er2x
r1=r2=r y=c1erx+c2xerx
r1 , r2 complex :α±iβ y=eαx(c1cosβx+c2sinβx

ii) Undetermined coefficients method:

i) If Gx=ekxPx,  where P  is a polynomial of degree n, then try yPx=ekxQx,  where Qx  is nth-degree polynomial.

ii) If Gx=ekxPxcosmx or Gx=ekxPxsinmx  where P  is a polynomial of degree n, then try yPx=ekxQxcosmx+ekxRxsinmx,  where Qx  and Rx nth-degree polynomial.

iii)

If any term of yP  is a solution of the complementary equation, multiply yP  by x  or by x2  if necessary

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Chapter 17 Solutions

Calculus (MindTap Course List)
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Ch. 17.1 - Solve the differential equation. 2d2ydt2+2dydty=0Ch. 17.1 - Solve the differential equation....Ch. 17.1 - Solve the differential equation....Ch. 17.1 - Graph the two basic solutions along with several...Ch. 17.1 - Graph the two basic solutions along with several...Ch. 17.1 - Graph the two basic solutions along with several...Ch. 17.1 - Solve the initial-value problem....Ch. 17.1 - Solve the initial-value problem....Ch. 17.1 - Solve the initial-value problem....Ch. 17.1 - Solve the initial-value problem....Ch. 17.1 - Solve the initial-value problem....Ch. 17.1 - Solve the initial-value problem....Ch. 17.1 - Solve the initial-value problem....Ch. 17.1 - Solve the initial-value problem....Ch. 17.1 - Solve the boundary-value problem, if possible....Ch. 17.1 - Solve the boundary-value problem, if possible....Ch. 17.1 - Solve the boundary-value problem, if possible....Ch. 17.1 - Solve the boundary-value problem, if possible....Ch. 17.1 - Solve the boundary-value problem, if possible....Ch. 17.1 - Solve the boundary-value problem, if possible....Ch. 17.1 - Solve the boundary-value problem, if possible....Ch. 17.1 - Solve the boundary-value problem, if possible....Ch. 17.1 - Let L be a nonzero real number. a Show that the...Ch. 17.1 - If a, b, and c are all positive constants and y(x)...Ch. 17.1 - Consider the boundary-value problem...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Graph the particular solution and several other...Ch. 17.2 - Graph the particular solution and several other...Ch. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Solve the differential equation using a...Ch. 17.2 - Solve the differential equation using a...Ch. 17.2 - Solve the differential equation using a...Ch. 17.2 - Solve the differential equation using a...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.2 - Solve the differential equation using the method...Ch. 17.3 - A spring has natural length 0.75 m and a 5-kg...Ch. 17.3 - 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 - Determine whether the statement is true or false....Ch. 17.R - Determine whether the statement is true or false....Ch. 17.R - Determine whether the statement is true or false....Ch. 17.R - Solve the differential equation. 4yy=0Ch. 17.R - Solve the differential equation. y2y+10y=0Ch. 17.R - Solve the differential equation. y+3y=0Ch. 17.R - Solve the differential equation. y+8y+16y=0Ch. 17.R - Solve the differential equation....Ch. 17.R - Solve the differential equation. d2ydx2+dydx2y=x2Ch. 17.R - Solve the differential equation....Ch. 17.R - Solve the differential equation. d2ydx2+4y=sin2xCh. 17.R - Solve the differential equation....Ch. 17.R - Solve the differential equation....Ch. 17.R - Solve the initial-value problem....Ch. 17.R - Solve the initial-value problem....Ch. 17.R - Solve the initial-value problem....Ch. 17.R - Solve the initial-value problem....Ch. 17.R - Solve the boundary-value problem, if possible....Ch. 17.R - Solve the boundary-value problem, if possible....Ch. 17.R - Use power series to solve the initial-value...Ch. 17.R - Use power series to solve the initial-value...Ch. 17.R - A Series circuit contains a resistor with R=40, an...Ch. 17.R - A spring with a mass of 2 kg has damping constant...Ch. 17.R - Assume that the earth is a solid sphere of uniform...

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