Solution Found!
In 1–4 the given family of functions is the general
Chapter 4, Problem 1E(choose chapter or problem)
In Problems 1–4 the given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem.
\(y=c_1e^x+c_2e^{-x},(-\infty,\ \ \ )\)
\(y^{\prime\prime}-y=0,\quad\ \ y(0)=0,\quad\ \ y^{\prime}(0)=1\)
Text Transcription:
y=c_1e^x+c_2e^{-x},(-\infty,\ \ \ )
y^{\prime\prime}-y=0,\quad\ \ y(0)=0,\quad\ \ y^{\prime}(0)=1
Questions & Answers
QUESTION:
In Problems 1–4 the given family of functions is the general solution of the differential equation on the indicated interval. Find a member of the family that is a solution of the initial-value problem.
\(y=c_1e^x+c_2e^{-x},(-\infty,\ \ \ )\)
\(y^{\prime\prime}-y=0,\quad\ \ y(0)=0,\quad\ \ y^{\prime}(0)=1\)
Text Transcription:
y=c_1e^x+c_2e^{-x},(-\infty,\ \ \ )
y^{\prime\prime}-y=0,\quad\ \ y(0)=0,\quad\ \ y^{\prime}(0)=1
ANSWER:Step 1 of 3
In this problem we have to determine the solution of the given differential equation given its initial conditions and family member.
Given differential equation
given initial conditions