   Chapter 8.1, Problem 50E

Chapter
Section
Textbook Problem

Slope Field In Exercises 49 and 50, 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 = 5 − y , y ( 0 ) = 1

To determine

To calculate: The slope field for the given differential equation and graph the solution satisfying the specified initial condition.

Explanation

Given:

We are given that dydx=5y, y(0)=1

Explanation:

Choose, y=54ex

Rearrange the given differential equation dydx=5y

dy5y=dx ……(1)

Integrate both sides of equation (1), we get that:

dy5y=dx

ln|5y|=x+C ……(2)

Now, use the initial conditions y(0)=1, that is y=1 when x=0, such that

ln|51|=0+C

C=ln4 ……(3)

Use equation (3) in equation (2),

ln|5y|=xln|4|ln|4|ln|5y|=x

Now, use the logarithmic rule ln|a|ln|b|=ln|

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