Explanation Given: y ' + 3 y = e 2 x and y ( 0 ) = − 1 Formula used: ∫ x n d x = 1 n + 1 x n + 1 ……………. (1) ∫ ( u ( x ) . v ( x ) ) d x = u ( x ) ∫ v ( x ) d x − ∫ u ' ( x ) ∫ v ( x ) d x ……………. (2) ∫ e x d x = e x + c …………… (3) Calculation: Consider the given equation y ' + 3 y = e 2 x ⇒ d y d x + 3 y = e 2 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 + 3 y = e 2 x P = 3 and Q = e 2 x I ...

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 10.5, Problem 21E

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The general solution of $y' + 3 y = e^{2 x}$

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Chapter 10.5, Problem 20E

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CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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The general solution of y ' + 3 y = e 2 x

Solution Summary: The author explains how the linear differential equations can be represented in the form of: d y = e 2 x + P.

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The general solution of $y' + 3 y = e^{2 x}$

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The general solution of y ' + 3 y = e 2 x

Solution Summary: The author explains how the linear differential equations can be represented in the form of: d y = e 2 x + P.

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The general solution of y'+3y=e2x

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The general solution of $y' + 3 y = e^{2 x}$