Explanation The given differential equation is y ″ + 3 y ′ = 4 x − 5 . The corresponding homogeneous differential is y ″ + 3 y ′ = 0 . The auxiliary equation of the homogeneous equation is m 2 + 3 m = 0 . Solve the auxiliary equation as follows. m 2 + 3 m = 0 m ( m + 3 ) = 0 m 1 = 0 , m 2 = − 3 Therefore, the complementary function is y c = c 1 + c 2 e − 3 x . Since, 4 x − 5 is annihilate by the differential operator D 2 , apply the differential operator D 2 to both sides of the equation y ″ + 3 y ′ = 4 x − 5 . D 2 ( D 2 + 3 D ) y = D 2 ( 4 x − 5 ) D 2 ( D 2 + 3 D ) y = 0 [ where D 2 ( 4 x − 5 ) = 0 ] The corresponding auxiliary equation is m 2 + 3 m and factors are given by m 2 + 3 m = 0 m 3 ( m + 3 ) = 0 m 1 = m 2 = m 3 = 0 , m 4 = − 3 Therefore, the general solution is y = c 1 + c 2 x + c 3 x 2 + c 4 e − 3 x . In order to find the particular solution y p of the given differential equation, observe that solutions y 1 = c 1 and y 4 = c 4 e − 3 x are duplicates within the set of solutions to the homogeneous equation above

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

11th Edition

ISBN: 9781305965720

Author: Dennis G. Zill

Publisher: Cengage Learning

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Chapter 4.5, Problem 40E

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To solve: The differential equation by undetermined coefficients.

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Chapter 4.5, Problem 39E

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Please conduct a step by step of these statistical tests on separate sheets of Microsoft Excel. If the calculations in Microsoft Excel are incorrect, the null and alternative hypotheses, as well as the conclusions drawn from them, will be meaningless and will not receive any points 2. Two-Sample T-Test: Compare the average sales revenue of two different regions to determine if there is a significant difference. (Hints: The null can be about maintaining status-quo or no difference among groups; if alternative hypothesis is non-directional use the two-tailed p-value from excel file to make a decision about rejecting or not rejecting null) H0 = H1=

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A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - In Problems 14 the given family of functions is...Ch. 4.1 - Given that y=c1+c2x2 is a two-parameter family of...Ch. 4.1 - Find two members of the family of solutions in...Ch. 4.1 - Given that x(t) = c1 cos t + c2 sin t is the...Ch. 4.1 - Use the general solution of x + 2x = 0 given in...Ch. 4.1 - In Problems 9 and 10 find an interval centered...Ch. 4.1 - In Problems 9 and 10 find an interval centered...

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