Explanation Given: x y ' = 2 y + x − 1 and y ( 3 2 ) = 9 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 x y ' = 2 y + x − 1 ⇒ x d y d x = 2 y + x − 1 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 − 2 y x = x − 1 x P = − 2 x and Q = x − 1 x I . F = e ∫ − 2 x d x ⇒ I . F = e ln ( 1 x 2 ) ⇒ I ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

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The general solution of $x y' = 2 y + x - 1$

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The general solution of x y ' = 2 y + x − 1

Solution Summary: The author explains that every linear differential equation can be represented in the form of: d y + x + P and integrating factor I.

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The general solution of $x y' = 2 y + x - 1$

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The general solution of x y ' = 2 y + x − 1

Solution Summary: The author explains that every linear differential equation can be represented in the form of: d y + x + P and integrating factor I.

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The general solution of xy'=2y+x−1

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Chapter 10 Solutions

The general solution of $x y' = 2 y + x - 1$