Explanation Formula used: tanh x = sinh x cosh x = e x − e − x 2 e x + e − x 2 = e x − e − x e x + e − x sech x = 1 cosh x = 1 e x + e − x 2 = 2 e x + e − x ∫ tanh x d x = ln ( cosh x ) + C Calculation: Consider the given equation y ' + ( tanh x ) y = 1 ⇒ d y d x + ( tanh x ) y = 1 According to linear differential equation, every linear differential equation can be represented in the form of: d y d x + P . y = Q Where P and Q are functions of x and integrating factor of given differential equation is I . F = e ∫ P d x and solution is given by y . e ∫ P d x = ∫ Q . e ∫ P d x d x Converting the given equation into standard form, we get d y d x + ( tanh x ) y = 1 Here, we have P = tanh x and Q = 1 I . F = e ∫ tanh x d x = e ∫ sinh x cosh x d x Let cosh x = t ⇒ sinh x d x = d t ⇒ e ∫ sinh x cosh x d x = e ∫ d t t = e log t = e log ( cosh x ) = cosh x ∴ I

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

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Chapter 10.5, Problem 27E

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The initial value solution of the given differential equation y'+(tanhx)y=1

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Chapter 10.5, Problem 26E

Chapter 10.5, Problem 28E

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Chapter 10 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

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The initial value solution of the given differential equation y ' + ( tanh x ) y = 1

Solution Summary: The author explains that the initial value solution of the given differential equation is y'+(mathrmtanh

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The initial value solution of the given differential equation y'+(tanhx)y=1

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