Explanation The given differential equation is t 2 y ″ + 3 t y ′ + y = 0 , t > 0 , y 1 ( t ) = t − 1 . Rewrite the equation in standard form as follows. t 2 y ″ + 3 t y ′ + y = 0 t 2 t 2 y ″ + 3 t t 2 y ′ + 1 t 2 y = 0 t 2 y ″ + 3 t y ′ + 1 t 2 y = 0 Compare y ″ + 3 t y ′ + 1 t 2 y = 0 with general form y ″ + p ( t ) y ′ + q ( t ) y = 0 . Here, p ( t ) = 3 t and q ( t ) = 1 t 2 . The Wronskian of y 1 and y 2 is computed as follows. Substitute p ( t ) = 3 t in w ( y 1 , y 2 ) = c e − ∫ p ( t ) d t . w ( y 1 , y 2 ) = c e − ∫ 3 t d t = c e − 3 ln t = c e ln t − 3 = c t − 3 Obtain the second solution as follows

Elementary Differential Equations And Boundary Value Problems, 11th Edition

11th Edition

ISBN: 9781119375753

Author: William E. Boyce, Richard C. DiPrima, Douglas B. Meade

Publisher: WILEY

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Question

Chapter 3.4, Problem 25P

To determine

The solution of the given differential equation using the method of reduction of order.

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Chapter 3.4, Problem 24P

Chapter 3.4, Problem 26P

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Chapter 3 Solutions

Elementary Differential Equations And Boundary Value Problems, 11th Edition

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