Chapter 6.1, Problem 78E

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

Euler's Method In Exercises 73-78, use Euler’s Method to make a table of values for the approximate solution of the differential equation with the specified initial value. Use n steps of size h. y ' = cos x + sin y , y ( 0 ) = 5 , n = 10 , h = 0.1

To determine

To Calculate: The approximate solution of the differential equation, y=cosx+siny with the specified initial value using Euler’s method where, y(0)=5,n=10,h=0.1.

Explanation

Given:

The differential equation’

y=cosx+siny,y(0)=5,n=10,h=0.1.

Formula used:

Euler’s method, yn=yn1+hF(xn1,yn1) at xn=xn1+h.

Calculation:

The differential equation’

y=cosx+siny

By the use of h=0.1,x0=0,y(0)=5, and F(x,y)=cosx+siny, we have

x0=0, x1=0.1, x2=0.2, x3=0.3, x4=0.4, x5=0.5, x6=0.6, x7=0.7, x8=0.8, x9=0.9, x10=1.0

The first three approximations are

y1=y0+hF(x0,y0)=5+0

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