Explanation Definition used: The first order linear equation is of the form d y d t + p ( t ) y = g ( t ) where p and g are function of the independent variable t . Formula used: The integrating factor μ ( t ) of the first order differential equation d y d t + p ( t ) y = g ( t ) is given as μ ( t ) = exp ∫ p ( t ) d t and the solution of the differential equation is given by y = 1 μ ( t ) [ ∫ μ ( s ) g ( s ) d s + c ] . Calculation: The given differential equation is y ′ + ( 2 t ) y = cos t t 2 with the initial value y ( π ) = 0 and t > 0 . By comparing the equation y ′ + ( 2 t ) y = cos t t 2 with its standard form d y d t + p ( t ) y = g ( t ) , it is obtained that p ( t ) = 2 t and g ( t ) = cos t t 2 . Compute the integrating factor μ ( t ) of the differential equation y ′ + ( 2 t ) y = cos t t 2 as follows. μ ( t ) = exp ∫ p ( t ) d t = exp ∫ 2 t d t = exp ( 2 ln t ) = t 2 ( ∵ a ln b = ln b a and

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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Chapter 2.1, Problem 11P

To determine

To solve: The initial value differential equation y′+(2t)y=costt2, y(π)=0 and t>0.

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Chapter 2.1, Problem 10P

Chapter 2.1, Problem 12P

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Chapter 2 Solutions

Elementary Differential Equations And Boundary Value Problems, 11th Edition

Ch. 2.1 - Prob. 1P Ch. 2.1 - Prob. 2P Ch. 2.1 - Prob. 3P Ch. 2.1 - Prob. 4P Ch. 2.1 - Prob. 5P Ch. 2.1 - Prob. 6P Ch. 2.1 - Prob. 7P Ch. 2.1 - Prob. 8P Ch. 2.1 - Prob. 9P Ch. 2.1 - Prob. 10P

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The initial value differential equation y ′ + ( 2 t ) y = cos t t 2 , y ( π ) = 0 and t &gt; 0 .

To solve: The initial value differential equation y′+(2t)y=costt2, y(π)=0 and t>0.

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Chapter 2 Solutions

The initial value differential equation y ′ + ( 2 t ) y = cos t t 2 , y ( π ) = 0 and t > 0 .