   Chapter 8.2, Problem 36E

Chapter
Section
Textbook Problem

# Slope Field In Exercises 39 and 40, a differential equation, a point, and a slope field are given.Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the given point. (To print an enlarged copy of the graph, go toMathGraphs.com.)Use integration and the given point to find the particular solution of the differential equation and use a graphing utility to graph the solution. Compare the result with the sketch in part (a) that passes through the given point. d y d x = e − x / 3 sin 2 x , ( 0 , − 18 37 ) .

a)

To determine

To graph: two approximate solutions of the differential equation on the slope field, one of which

passes through the given point.

Explanation

Given: dydx=ex/3sin2x, the point (0,1837) and the graph

Refer to the question for figure.

Graph:

Using a graphing utility tool, the graph of the differential equation is plotted as shown below

b)

To determine

To calculate: the particular solution of the given differential equation and graph the solution using a graphing utility tool.

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