Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
In following Equation, solve the initial value problem.
4y" - 4y' + y = 0, y(0) = -1, y'(0) = 2
Expert Solution
Step 1
the given differential equation is:
we have to solve the initial value problem
y(0)=-1 and y'(0)=2
Step 2
the given differential equation is:
the differential equation can be written as:
as we know that
Step 3
therefore,
therefore the function in differential operator is f(D) and is given by
now put D=m in the f(D)
therefore,
now equate f(m)=0
the equation f(m)=0 is called the auxiliary equation.
therefore,
Step 4
therefore is the repeated root of the auxiliary equation.
therefore the general solution of the given differential equation is:
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