Chapter 9.3, Problem 28E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

**27–28**

(a) Use a computer algebra system to draw a direction field for the differential equation. Get a printout and use it to sketch some solution curves without solving the differential equation.

(b) Solve the differential equation.

(c) Use the CAS to draw several members of the family of solutions obtained in part (b). Compare with the curves from part (a).

To determine

**To draw:**

A direction field for the given differential equation and then sketch some solution curves without solving the differential equation.

Explanation

**1) Concept:**

Use Mathematica to draw a direction field and then sketch some solution curves with your hand.

**2) Given:**

**3) Calculation:**

To draw direction field, use below command in Mathematica

then output is

Now, draw some solution curves with hand without solving the differential equation is

**Conclusion:**

The graph of directional field using Mathematica is

And graph of some solution curves with hand without solving the differential equation is

**To solve:**

The given differential equation

**Solution:**

**1) Concept:**

To solve the differential equation of the form

Sect-9.1 P-1ESect-9.1 P-2ESect-9.1 P-3ESect-9.1 P-4ESect-9.1 P-5ESect-9.1 P-6ESect-9.1 P-7ESect-9.1 P-8ESect-9.1 P-9ESect-9.1 P-10E

Sect-9.1 P-11ESect-9.1 P-12ESect-9.1 P-13ESect-9.1 P-14ESect-9.1 P-15ESect-9.1 P-16ESect-9.1 P-17ESect-9.2 P-1ESect-9.2 P-2ESect-9.2 P-3ESect-9.2 P-4ESect-9.2 P-5ESect-9.2 P-6ESect-9.2 P-7ESect-9.2 P-8ESect-9.2 P-9ESect-9.2 P-10ESect-9.2 P-11ESect-9.2 P-12ESect-9.2 P-13ESect-9.2 P-14ESect-9.2 P-15ESect-9.2 P-16ESect-9.2 P-17ESect-9.2 P-18ESect-9.2 P-19ESect-9.2 P-20ESect-9.2 P-21ESect-9.2 P-22ESect-9.2 P-23ESect-9.2 P-24ESect-9.2 P-25ESect-9.2 P-26ESect-9.2 P-27ESect-9.2 P-28ESect-9.3 P-1ESect-9.3 P-2ESect-9.3 P-3ESect-9.3 P-4ESect-9.3 P-5ESect-9.3 P-6ESect-9.3 P-7ESect-9.3 P-8ESect-9.3 P-9ESect-9.3 P-10ESect-9.3 P-11ESect-9.3 P-12ESect-9.3 P-13ESect-9.3 P-14ESect-9.3 P-15ESect-9.3 P-16ESect-9.3 P-17ESect-9.3 P-18ESect-9.3 P-19ESect-9.3 P-20ESect-9.3 P-21ESect-9.3 P-22ESect-9.3 P-23ESect-9.3 P-24ESect-9.3 P-25ESect-9.3 P-26ESect-9.3 P-27ESect-9.3 P-28ESect-9.3 P-29ESect-9.3 P-30ESect-9.3 P-31ESect-9.3 P-32ESect-9.3 P-33ESect-9.3 P-34ESect-9.3 P-35ESect-9.3 P-36ESect-9.3 P-37ESect-9.3 P-38ESect-9.3 P-39ESect-9.3 P-40ESect-9.3 P-41ESect-9.3 P-42ESect-9.3 P-43ESect-9.3 P-44ESect-9.3 P-45ESect-9.3 P-46ESect-9.3 P-47ESect-9.3 P-48ESect-9.3 P-49ESect-9.3 P-50ESect-9.3 P-51ESect-9.3 P-52ESect-9.3 P-53ESect-9.3 P-54ESect-9.4 P-1ESect-9.4 P-2ESect-9.4 P-3ESect-9.4 P-4ESect-9.4 P-5ESect-9.4 P-6ESect-9.4 P-7ESect-9.4 P-8ESect-9.4 P-9ESect-9.4 P-10ESect-9.4 P-11ESect-9.4 P-12ESect-9.4 P-13ESect-9.4 P-14ESect-9.4 P-15ESect-9.4 P-16ESect-9.4 P-17ESect-9.4 P-18ESect-9.4 P-19ESect-9.4 P-20ESect-9.4 P-21ESect-9.4 P-22ESect-9.4 P-23ESect-9.4 P-24ESect-9.4 P-25ESect-9.5 P-1ESect-9.5 P-2ESect-9.5 P-3ESect-9.5 P-4ESect-9.5 P-5ESect-9.5 P-6ESect-9.5 P-7ESect-9.5 P-8ESect-9.5 P-9ESect-9.5 P-10ESect-9.5 P-11ESect-9.5 P-12ESect-9.5 P-13ESect-9.5 P-14ESect-9.5 P-15ESect-9.5 P-16ESect-9.5 P-17ESect-9.5 P-18ESect-9.5 P-19ESect-9.5 P-20ESect-9.5 P-21ESect-9.5 P-22ESect-9.5 P-23ESect-9.5 P-24ESect-9.5 P-25ESect-9.5 P-26ESect-9.5 P-27ESect-9.5 P-28ESect-9.5 P-29ESect-9.5 P-30ESect-9.5 P-31ESect-9.5 P-32ESect-9.5 P-33ESect-9.5 P-34ESect-9.5 P-35ESect-9.5 P-36ESect-9.5 P-37ESect-9.5 P-38ESect-9.6 P-1ESect-9.6 P-2ESect-9.6 P-3ESect-9.6 P-4ESect-9.6 P-5ESect-9.6 P-6ESect-9.6 P-7ESect-9.6 P-8ESect-9.6 P-9ESect-9.6 P-10ESect-9.6 P-11ESect-9.6 P-12ESect-9.R P-1CCSect-9.R P-2CCSect-9.R P-3CCSect-9.R P-4CCSect-9.R P-5CCSect-9.R P-6CCSect-9.R P-7CCSect-9.R P-8CCSect-9.R P-9CCSect-9.R P-1TFQSect-9.R P-2TFQSect-9.R P-3TFQSect-9.R P-4TFQSect-9.R P-5TFQSect-9.R P-6TFQSect-9.R P-7TFQSect-9.R P-1ESect-9.R P-2ESect-9.R P-3ESect-9.R P-4ESect-9.R P-5ESect-9.R P-6ESect-9.R P-7ESect-9.R P-8ESect-9.R P-9ESect-9.R P-10ESect-9.R P-11ESect-9.R P-12ESect-9.R P-13ESect-9.R P-14ESect-9.R P-15ESect-9.R P-16ESect-9.R P-17ESect-9.R P-18ESect-9.R P-19ESect-9.R P-20ESect-9.R P-21ESect-9.R P-22ESect-9.R P-23ESect-9.R P-24ESect-9.P P-1PSect-9.P P-2PSect-9.P P-3PSect-9.P P-4PSect-9.P P-5PSect-9.P P-6PSect-9.P P-7PSect-9.P P-8PSect-9.P P-9PSect-9.P P-10PSect-9.P P-11PSect-9.P P-12PSect-9.P P-13PSect-9.P P-14PSect-9.P P-15PSect-9.P P-16P

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