Explanation Given: The given initial value problem is, d y d t + 2 y = 1 y ( 0 ) = 5 2 Definition: “A solution in which the dependent variable is expressed solely in terms of the independent variable and constant is said to be an explicit solution.” Calculation: Consider the differential equation. d y d t + 2 y = 1 Rewrite the differential equation in the form as. d y d t = 1 − 2 y d y 1 − 2 y = d t Integrate on both sides of the equation. ∫ d y 1 − 2 y = ∫ d t − 1 2 ln ( 1 − 2 y ) = t + c ln ( 1 − 2 y ) = − 2 ( t + c ) ( 1 − 2 y ) = e − 2 ( t + c ) Relabel e − 2 c = C

6th Edition

ISBN: 9781284127003

Author: ZILL

Publisher: JONES+BARTLETT LEARNING,LLC (CC)

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Chapter 2.2, Problem 26E

To determine

The explicit solution of the given initial value problem.

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Chapter 2.2, Problem 25E

Chapter 2.2, Problem 27E

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The explicit solution of the given initial value problem.

Solution Summary: The author explains the explicit solution of the given initial value problem: underset_y=1+4e-2t2.

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The explicit solution of the given initial value problem.

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Chapter 2 Solutions