Explanation Given: y ' + n y = e m x Formula used: ∫ x n d x = 1 n + 1 x n + 1 ……………. (1) ∫ 1 x d x = ln x + c …………… (2) Calculation: Consider the given equation y ' + n y = e m x ⇒ d y d x + n y = e m x 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 I . F = e ∫ P d x And solution is e ∫ P d x . y = ∫ Q . e ∫ P d x d x Converting the given equation into standard form d y d x + n y = e m x P = n and Q = e m x I ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Differential Equations

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Chapter 10.4, Problem 27E

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The general solution of $y' + n y = e^{m x}$

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The general solution of y ' + n y = e m x

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The general solution of $y' + n y = e^{m x}$