Explanation Given: Initial value problem is, d y d x = 2 x + 1 2 y , y ( − 2 ) = − 1 . Procedure used: Use variable separation method to solve given initial value problem. Calculation: Separate the variables of given initial value problem. d y d x = 2 x + 1 2 y 2 y d y = ( 2 x + 1 ) d x (1) Integrate equation (1). ∫ 2 y d y = ∫ ( 2 x + 1 ) d x 2 y 2 2 = 2 x 2 2 + x + C y 2 = x 2 + x + C (2) Here, C is constant of integration . Substitute − 1 for y and − 2 for x in equation (2). ( − 1 ) 2 = ( − 2 ) 2 + ( − 2 ) + C 1 = 4 − 2 + C C = 1 − 4 + 2 C = − 1 Substitute − 1 for C in equation (2). y 2 = x 2 + x − 1 y = x 2 + x − 1 Thus, the general solution to the given initial value problem is y = x 2 + x − 1

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Differential Equations

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Chapter 2.2, Problem 31E

To determine

To find: An explicit solution of given initial value problem and exact interval of definition by analytical method. Also plot the graph of the solution.

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Chapter 2.2, Problem 30E

Chapter 2.2, Problem 32E

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EBK ADVANCED ENGINEERING MATHEMATICS

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