Solution Found!
Solved: In 11 –14, y = c1ex + c2e-x is a two-parameter
Chapter 1, Problem 12E(choose chapter or problem)
In Problems 11–14, \(y=c_{1} e^{x}+c_{2} e^{-x}\) is a two-parameter family of solutions of the second-order DE \(y^{\prime \prime}-y=0\). Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions.
y(1)=0, \(y^{\prime}(1)=e\)
Text Transcription:
y=c_1 e^x + c_2 e^-x
y^prime prime - y = 0
y^prime(1)=e
Questions & Answers
QUESTION:
In Problems 11–14, \(y=c_{1} e^{x}+c_{2} e^{-x}\) is a two-parameter family of solutions of the second-order DE \(y^{\prime \prime}-y=0\). Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions.
y(1)=0, \(y^{\prime}(1)=e\)
Text Transcription:
y=c_1 e^x + c_2 e^-x
y^prime prime - y = 0
y^prime(1)=e
ANSWER:Step 1 of 6
Given that
We have to find a solution of the second-order IVP consisting of the given initial conditions and this differential equation.