Explanation Given: d y d x = y x + x and y ( 1 ) = 3 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 d y d x = y x + x According to the rule of linear differential equations, 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 − y x = x P = − 1 x and Q = 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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The general solution of d y d t = y + t 2

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