(a) Explanation Given: Initial value problem is, d y d x = y 2 − 4 y ( 0 ) = 2 , y ( 0 ) = − 2 , y ( 1 4 ) = 1 . Procedure used: Use variable separable method to solve given initial value problem. Calculation: Separate the variables of given initial value problem. d y d x = y 2 − 4 d y y 2 − 4 = d x d y y 2 − 2 2 = d x d y ( y − 2 ) ( y + 2 ) = d x Further, simplify the above equation, [ ( 1 4 ) y − 2 − ( 1 4 ) y + 2 ] d y = d x [ 1 4 ( y − 2 ) − 1 4 ( y + 2 ) ] d y = d x 1 4 [ 1 ( y − 2 ) − 1 ( y + 2 ) ] d y = d x (1) Integrate equation (1), 1 4 ∫ [ 1 ( y − 2 ) − 1 ( y + 2 ) ] d y = ∫ d x 1 4 [ ln | y − 2 | − ln | y + 2 | ] = x + C 1 1 4 ln | y − 2 y + 2 | = x + C 1 ln | y − 2 y + 2 | = 4 x + 4 C 1 (2) Here, constant of integration is C 1 . Substitute C 2 for 4 C 1 in equation (2). ln | y − 2 y + 2 | = 4 x + C 2 | y − 2 y + 2 | = e 4 x + C 2 y − 2 y + 2 = ± e 4 x + C 2 y − 2 y + 2 = ± e C 2 e 4 x (3) Substitute K for ± e C 2 in equation (3) (b) To determine The explicit solution of given initial value problem.

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.2, Problem 35E

(a)

To determine

The explicit solution of given initial value problem.

(b)

To determine

The explicit solution of given initial value problem.

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Chapter 2.2, Problem 34E

Chapter 2.2, Problem 36E

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Chapter 2 Solutions

Advanced Engineering Mathematics

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