Show that is a solution to dy/dx – 3y = -3 for any choice

Chapter 1, Problem 17E

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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

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.

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