Explanation Procedure used: The standard form of the linear differential equation: d y d x + P ( x ) y = f ( x ) The integrating factor for above equation is e ∫ P ( x ) d x . Calculation: Consider the given differential equation. y ′ + 2 x y = x 3 (1) Compare the above equation with standard equation. P ( x ) = 2 x and f ( x ) = x 3 Calculate the integrating factor for the equation. e ∫ P ( x ) d x = e ∫ 2 x d x = e 2 ( x 2 2 ) = e x 2 Multiply equation (1) with integrating factor. y ′ e x 2 + 2 x e x 2 y = e x 2 x 3 d d x [ e x 2 y ] = e x 3 x 2 Integrate on both sides of the equation. ∫ d d x [ e x 2 y ] d x = ∫ e x 2 x 3 d x e x 2 y = ∫ e x 2 x 3 d x Substitute t for x 2 and 2 x d x = d t in above equation

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Differential Equations

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Chapter 2.3, Problem 6E

To determine

The general solution of differential equation, largest interval over which solution is defined and transient term in the general solution of differential equation.

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Chapter 2.3, Problem 5E

Chapter 2.3, Problem 7E

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EBK ADVANCED ENGINEERING MATHEMATICS

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