Explanation Procedure used: Solution to a differential equation. The n th-order ordinary differential equation is one dependent variable by the general form, F ( x , y , y ' , ... , y ( n ) ) = 0 Where F is a real valued function of n + 2 variables: x , y , y ' , ... , y ( n ) . The solution of an n th-order ordinary differential equation is a function ϕ that possesses at least n derivatives and satisfying the differential equation on interval I , i.e. F ( x , ϕ ( x ) , ϕ ' ( x ) , ... , ϕ ( n ) ( x ) ) = 0 for all x in I . Calculation: Consider the given differential equation y = 6 5 − 6 5 e − 20 t and the given function d y d t + 20 y = 24

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 1.1, Problem 12E

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To verify: The function dydt+20y=24 is a solution of the differential equation y=65−65e−20t.

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Chapter 1.1, Problem 11E

Chapter 1.1, Problem 13E

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To verify: The function d y d t + 20 y = 24 is a solution of the differential equation y = 6 5 − 6 5 e − 20 t .

Solution Summary: The author explains the solution of the nth-order ordinary differential equation, where F is a real valued function of n+2 variables.

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To verify: The function dydt+20y=24 is a solution of the differential equation y=65−65e−20t.

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Chapter 1 Solutions