To determine The y -values of the solution for the values of x and Δ x by using of Euler’s method, and plot the graphs of the solutions. Explanation Formula used: To find an approximate solution to a differential equation of the form d y d x = f ( x , y ) , that passes through a known point ( x 0 , y 0 ) . Then the next value of ( x n , y n ) is y n + 1 = y n + f ( x n , y n ) Δ x and x n + 1 = x n + Δ x . Calculation: The approximate solution of a differential equation passes through ( x 0 , y 0 ) = ( 0 , 1 ) , write the differential equation d y d x = x + 1 as d y = ( x + 1 ) d x and then approximate d y as y 1 − y 0 , and d x is replaced as Δ x . Therefore, write the differential equation as ( y 1 − y 0 ) = ( x + 1 ) Δ x . Transpose y 0 to right hand side as ( y 1 ) = y 0 + ( x 0 + 1 ) Δ x and x 1 = x 0 + Δ x . Substitute x 0 , y 0 and Δ x in above two equation. y 1 = y 0 + ( x 0 + 1 ) Δ x = 1 + ( 0 + 1 ) 0.2 = 1.2 The value of x 1 is calculated as, x 1 = x 0 + Δ x = 0 + 0.2 = 0.2 Thus, the curve passes through ( x 1 , y 1 ) = ( 0.2 , 1.2 ) . Now use point ( x 1 , y 1 ) to find the next point on the curve, which is ( x 2 , y 2 ) . y 2 = y 1 + ( x 1 + 1 ) Δ x = 1.2 + ( 0.2 + 1 ) 0.2 = 1.44 The value of x 2 is calculated as, x 2 = x 1 + Δ x = 0.2 + 0.2 = 0.4 Thus, the curve passes through ( x 2 , y 2 ) = ( 0.4 , 1.44 ) . Similarly, now use point ( x 2 , y 2 ) to find the next point on the curve, which is ( x 3 , y 3 ) . y 3 = y 2 + ( x 2 + 1 ) Δ x = 1.44 + ( 0

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 31.5, Problem 1E

To determine

The y-values of the solution for the values of x and Δx by using of Euler’s method, and plot the graphs of the solutions.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 31.4, Problem 42E

Chapter 31.5, Problem 2E

Students have asked these similar questions

Question Find the following limit. Select the correct answer below: 1 2 0 4 5x lim sin (2x)+tan 2 x→

A quality characteristic of a product is normally distributed with mean μ and standard deviation σ = 1. Speci- fications on the characteristic are 6≤x≤8. A unit that falls within specifications on this quality characteristic results in a profit of Co. However, if x 8, the profit is -C2. Find the value ofμ that maximizes the expected profit.

A) The output voltage of a power supply is normally distributed with mean 5 V and standard deviation 0.02 V. If the lower and upper specifications for voltage are 4.95 V and 5.05 V, respectively, what is the probability that a power supply selected at random conform to the specifications on voltage? B) Continuation of A. Reconsider the power supply manufacturing process in A. Suppose We wanted to improve the process. Can shifting the mean reduce the number of nonconforming units produced? How much would the process variability need to be reduced in order to have all but one out of 1000 units conform to the specifications?

Chapter 31 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 31.1 - Show that is a solution of . Is it the general...Ch. 31.1 - Prob. 1E Ch. 31.1 - In Exercises 1 and 2, show that the indicated...Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 4E Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 6E Ch. 31.1 - In Exercises 7–10, show that each function y =...Ch. 31.1 - Prob. 8E Ch. 31.1 - In Exercises 7–10, show that each function y =...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.