Explanation Given: t y ' ' − ( t + 1 ) y ' + y = t 2 ... ( 1 ) and the linearly independent solutions to the homogeneous differential equation for t > 0 are y 1 = e t , y 2 = t + 1 . Approach: Since, y 1 = e t , y 2 = t + 1 are the linearly independent solutions to the corresponding homogeneous equation, ∴ right hand side of equation (1) has the general solution of the form y

Fundamentals of Differential Equations and Boundary Value Problems

7th Edition

ISBN: 9780321977106

Author: Nagle, R. Kent

Publisher: Pearson Education, Limited

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Chapter 4.6, Problem 23E

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General solution to the differential equation.

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Chapter 4.6, Problem 22E

Chapter 4.6, Problem 24E

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Fundamentals of Differential Equations and Boundary Value Problems

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General solution to the differential equation.

Solution Summary: The author explains that the linearly independent solutions to the homogeneous differential equation are y_1=et.

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General solution to the differential equation.