Explanation Given: In the interval of [ 0 , 1 ] the function have 20 subintervals as h = 0.05 . The differential equation is d y d x = 2 x y ; y ( 0 ) = 3 . Definition used: If y = f ( x ) is the solution of a differential equation d y d x = g ( x , y ) with y ( x 0 ) = y 0 . Assume, for an interval [ x 0 , x n ] , x i + 1 = x i + h and y i + 1 = y i + g ( x i , y i ) h , where 0 ≤ i ≤ n − 1 . Then f ( x i + 1 ) ≈ y i + 1 . Calculation: Substitute 0 for x 0 and 0.05 for h to obtain the value of x 1 as follows: x 1 = x 0 + h = 0 + 0.05 = 0.05 Substitute x 0 for x and y 0 for y in g ( x , y ) to obtain the value of g ( x 0 , y 0 ) as follows: g ( x 0 , y 0 ) = 2 x 0 y 0 Substitute 0 for x 0 and 3 for y 0 in g ( x 0 , y 0 ) as follows: g ( x 0 , y 0 ) = 2 ⋅ 0 3 = 0 Now substitute 3 for y 0 , 0 for g ( x 0 , y 0 ) and 0.05 for h to obtain the value of y 1 as follows: y 1 = y 0 + g ( x 0 , y 0 ) ⋅ h = 3 + 0 × 0.05 = 3 Substitute 3 for y 1 , 0.05 for x 1 to calculate the value of g ( x 1 , y 1 ) . g ( x 1 , y 1 ) = 2 x 1 y 1 = 2 × 0.05 3 = 0.03333 Now substitute 3 for y 1 , 0.03333 for g ( x 1 , y 1 ) and 0.05 for h to obtain the value of y 2 as follows: y 2 = y 1 + g ( x 1 , y 1 ) h = 3 + 0.0333 × 0.05 = 3.00167 Similarly, further values can also be calculated using the above steps. The below table shows all the values of x i and y i , i x i y i = y ( x i ) 0 0 3 1 0

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

11th Edition

ISBN: 9780133886849

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Concept explainers

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

Videos

Question

Chapter 10.3, Problem 20E

To determine

The approximate value of the indicated function y(0.6), value of y6−f(x6) using h=0.05 and then compare the result with Question 16.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.3, Problem 19E

Chapter 10.3, Problem 21E

Students have asked these similar questions

2) Integrate: 3x-5 Inx dx

If a = (4, 0, -1), find a vector b such that comp_b = 3. b =

For the vectors a = {2, 8} and b = {4, 6}, find orthab.

Chapter 10 Solutions

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

Ch. 10.1 - Find all solutions of the differential equation . Ch. 10.1 - Prob. 2YT Ch. 10.1 - Prob. 3YT Ch. 10.1 - Prob. 4YT Ch. 10.1 - Prob. 1WE Ch. 10.1 - Prob. 2WE Ch. 10.1 - Prob. 3WE Ch. 10.1 - Prob. 4WE Ch. 10.1 - Prob. 5WE Ch. 10.1 - Find the general solution for each differential...

Knowledge Booster

$Calculus$

Learn more about

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

The approximate value of the indicated function y ( 0.6 ) , value of y 6 − f ( x 6 ) using h = 0.05 and then compare the result with Question 16.

Concept explainers

Videos

The approximate value of the indicated function y(0.6), value of y6−f(x6) using h=0.05 and then compare the result with Question 16.

Want to see the full answer?

Chapter 10 Solutions