Solution Found!
Show that is a solution to dy/dx – 3y = -3 for any choice
Chapter 1, Problem 17E(choose chapter or problem)
Show that \(\phi(x)=C e^{3 x}+1\) is a solution to \(d y / d x-3 y=-3\) for any choice of the constant C. Thus, \(C e^{3 x}+1\) is a one-parameter family of solutions to the differential equation. Graph several of the solution curves using the same coordinate axes.
Equation Transcription:
𝜙
Text Transcription:
phi(x)=Ce^3x+1
dy/dx-3y=-3
Ce^3x+1
Questions & Answers
QUESTION:
Show that \(\phi(x)=C e^{3 x}+1\) is a solution to \(d y / d x-3 y=-3\) for any choice of the constant C. Thus, \(C e^{3 x}+1\) is a one-parameter family of solutions to the differential equation. Graph several of the solution curves using the same coordinate axes.
Equation Transcription:
𝜙
Text Transcription:
phi(x)=Ce^3x+1
dy/dx-3y=-3
Ce^3x+1
ANSWER:Solution:
Step 1
In this problem, we need to show that is one-parameter family of implicit solutions, where C is a nonzero constant to the given differential equation.
We are also asked to graph the solution curves.