Explanation 1) Concept: The general solution of nonhomogeneous differential equation is a y ' ' + b y ' + c y = G x can be written as y x = y c + y P Where y c is the general solution of complementary equation; a y ' ' + b y ' + c y = 0 and y P is a particular solution of a y ' ' + b y ' + c y = G x Find y c & y P i) General solution of a y ' ' + b y ' + c y = 0 : Roots of a r 2 + b r + c = 0 General solution r 1 , r 2 are real and distinct y = c 1 e r 1 x + c 2 e r 2 x r 1 = r 2 = r y = c 1 e r x + c 2 x e r x r 1 , r 2 c o m p l e x : α ± i β y = e α x ( c 1 c o s β x + c 2 s i n β x ii) Method of undetermined coefficient: It is reasonable to guess that there is a particular solution y P that is a polynomial of the same degree as G because if y is a polynomial, then a y ' ' + b y ' + c y is also a polynomial. We therefore substitute y P x = a polynomial into (Of the same degree as) the differential equation and determine the coefficient. 2) Given: The differential equation y ' ' - 3 y ' = sin ⁡ 2 x 3) Calculations: The given differential equation is y ' ' - 3 y ' = sin ⁡ 2 x The auxiliary equation of the homogeneous differential equation is r 2 - 3 r = 0 Solving the auxiliary equation r 2 - 3 r = 0 r r - 3 = 0 r = 0 , 3 Therefore, by concept (2) the complementary solution is y c = c 1 + c 2 e 3 x Now to find the particular solution of given differential equation, By using

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ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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Chapter 17.2, Problem 2E

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The differential equation y''-3y'=sin⁡2x

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Ch. 17.1 - Solve the differential equation. yy6y=0 Ch. 17.1 - Solve the differential equation. y6y+9y=0 Ch. 17.1 - Solve the differential equation. y+2y=0 Ch. 17.1 - Solve the differential equation. y+y12y=0 Ch. 17.1 - Solve the differential equation. 4y+4y+y=0 Ch. 17.1 - Solve the differential equation. 9y+4y=0 Ch. 17.1 - Solve the differential equation. 3y=4y Ch. 17.1 - Solve the differential equation. y=y Ch. 17.1 - Solve the differential equation. y4y+13y=0 Ch. 17.1 - Prob. 10E

Ch. 17.1 - Prob. 11E Ch. 17.1 - Prob. 12E Ch. 17.1 - Prob. 13E Ch. 17.1 - Prob. 14E Ch. 17.1 - Prob. 15E Ch. 17.1 - Prob. 16E Ch. 17.1 - Prob. 17E Ch. 17.1 - Prob. 18E Ch. 17.1 - Prob. 19E Ch. 17.1 - Prob. 20E Ch. 17.1 - Prob. 21E Ch. 17.1 - Prob. 22E Ch. 17.1 - Prob. 23E Ch. 17.1 - Prob. 24E Ch. 17.1 - Prob. 25E Ch. 17.1 - Prob. 26E Ch. 17.1 - Prob. 27E Ch. 17.1 - Prob. 28E Ch. 17.1 - Prob. 29E Ch. 17.1 - Prob. 30E Ch. 17.1 - Prob. 31E Ch. 17.1 - Prob. 32E Ch. 17.1 - Let L be a nonzero real number. a Show that the...Ch. 17.1 - Prob. 34E Ch. 17.1 - Consider the boundary-value problem...Ch. 17.2 - Solve the differential equation or initial-value...Ch. 17.2 - Prob. 2E Ch. 17.2 - Prob. 3E Ch. 17.2 - Prob. 4E Ch. 17.2 - Prob. 5E Ch. 17.2 - Prob. 6E Ch. 17.2 - Prob. 7E Ch. 17.2 - Prob. 8E Ch. 17.2 - Prob. 9E Ch. 17.2 - Prob. 10E Ch. 17.2 - Prob. 11E Ch. 17.2 - Prob. 12E Ch. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Prob. 14E Ch. 17.2 - Prob. 15E Ch. 17.2 - Prob. 16E Ch. 17.2 - Prob. 17E Ch. 17.2 - Write a trial solution for the method of...Ch. 17.2 - Prob. 19E Ch. 17.2 - Prob. 20E Ch. 17.2 - Prob. 21E Ch. 17.2 - Prob. 22E Ch. 17.2 - Prob. 23E Ch. 17.2 - Prob. 24E Ch. 17.2 - Prob. 25E Ch. 17.2 - Prob. 26E Ch. 17.2 - Prob. 27E Ch. 17.2 - Prob. 28E Ch. 17.3 - Prob. 1E Ch. 17.3 - Prob. 2E Ch. 17.3 - Prob. 3E Ch. 17.3 - Prob. 4E Ch. 17.3 - Prob. 5E Ch. 17.3 - For the spring in Exercise 4, find the damping...Ch. 17.3 - Prob. 7E Ch. 17.3 - Prob. 8E Ch. 17.3 - Prob. 9E Ch. 17.3 - Prob. 10E Ch. 17.3 - Prob. 11E Ch. 17.3 - Prob. 12E Ch. 17.3 - A series circuit consists of a resistor with R=20,...Ch. 17.3 - Prob. 14E Ch. 17.3 - Prob. 15E Ch. 17.3 - Prob. 16E Ch. 17.3 - Prob. 17E Ch. 17.3 - The figure shows a pendulum with length L and the...Ch. 17.4 - Prob. 1E Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Prob. 3E Ch. 17.4 - Prob. 4E Ch. 17.4 - Prob. 5E Ch. 17.4 - Prob. 6E Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Use power series to solve the differential...Ch. 17.4 - Prob. 9E Ch. 17.4 - Prob. 10E Ch. 17.4 - Prob. 11E Ch. 17.4 - The solution of the initial-value problem...Ch. 17.R - Prob. 1CC Ch. 17.R - Prob. 2CC Ch. 17.R - Prob. 3CC Ch. 17.R - Prob. 4CC Ch. 17.R - Prob. 5CC Ch. 17.R - Prob. 1TFQ Ch. 17.R - Prob. 2TFQ Ch. 17.R - Prob. 3TFQ Ch. 17.R - Prob. 4TFQ Ch. 17.R - Prob. 1E Ch. 17.R - Prob. 2E Ch. 17.R - Prob. 3E Ch. 17.R - Prob. 4E Ch. 17.R - Prob. 5E Ch. 17.R - Prob. 6E Ch. 17.R - Prob. 7E Ch. 17.R - Prob. 8E Ch. 17.R - Prob. 9E Ch. 17.R - Solve the differential equation....Ch. 17.R - Prob. 11E Ch. 17.R - Solve the initial-value problem....Ch. 17.R - Prob. 13E Ch. 17.R - Solve the initial-value problem....Ch. 17.R - Prob. 15E Ch. 17.R - Prob. 16E Ch. 17.R - Prob. 17E Ch. 17.R - Use power series to solve the initial-value...Ch. 17.R - Prob. 19E Ch. 17.R - Prob. 20E Ch. 17.R - Assume that the earth is a solid sphere of uniform...

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The differential equation y ' ' - 3 y ' = sin ⁡ 2 x

Solution Summary: The author explains that the general solution of the nonhomogeneous differential equation is ay'+b

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To solve: The differential equation y''-3y'=sin⁡2x

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Chapter 17 Solutions

To solve:

The differential equation y''-3y'=sin⁡2x