   Chapter 8.3, Problem 40E

Chapter
Section
Textbook Problem

# Slope Field In Exercises 41 and 42, use a computer algebra system to graph the slope field for the differential equation and graph the solution satisfying the specified initial condition. d y d x = 3 y tan 2 x , y ( 0 ) = 3

To determine

To graph: The slope field for the provided differential equation and the solution satisfying the

specified initial condition.

Explanation

Given: The provided differential equation is as follows;

dydx=3ytan2x, y(0)=3

Graph:

Consider the provided differential equation dydx=3ytan2x

Now rearrange this differential equation as follows;

dydx=3ytan2x to get y1/2dy=3tan2xdx ---------(1)

Thus this differential equation has changed into variable separable form.

Now, integrate both sides of equation (1), we get

y1/2dy=3tan2xdx.

2y=3(sec2x1)dx.

2y=3sec2xdx3dx

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