Chapter 8.1, Problem 47E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Slope Field In Exercises 47 and 48, a differential equation, a point, and a slope field are given, (a) 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 to McthGraphs.com.) (b) 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 s d t = t 1 − x 4 , ( 0 , − 1 2 )

(a)

To determine

To calculate: The solution of the differential equation on the slope field.

Explanation

Given:

dsdt=t1âˆ’t4,(0,âˆ’12) And the slope field,

Calculation:

Let us consider the differential equation,

dsdt=t1âˆ’t4

Solve this differential equation for t,

dsdt=t1âˆ’t4â‡’ds=t1âˆ’t4dt

The above equation is of variable separable form

(b)

To determine

To calculate: The particular solution by finding it.

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