To determine The value of y ( 1 ) and also to estimate the exact value of y ( 1 ) by using Euler method. Explanation Formula used: The first approximation of Euler’s method is given by y 1 = L ( x 1 ) = y 0 + f ( x 0 , y 0 ) d x . The second approximation of Euler’s method is given by y 2 = y 1 + f ( x 1 , y 1 ) d x . The third approximation of Euler’s method is given by y 3 = y 2 + f ( x 2 , y 2 ) d x . Calculation: The function is y ′ = y , y ( 0 ) = 1 and d x = 0.2 . Since y ( 0 ) = 1 , x 0 = 0 and y 0 = 1 . Evaluate the value of y ( 0.2 ) or first approximation as follows. y 1 = y 0 + f ( x 0 , y 0 ) d x = y 0 + y 0 d x = 1 + 1 ( 0.2 ) ( ∵ x 0 = 0 , y 0 = 1 and d x = 0.2 ) = 1 + 0.2 = 1.2 Thus, the first approximation is 1.2. Evaluate the value of y ( 0.4 ) or second approximation as follows. y 2 = y 1 + f ( x 1 , y 1 ) d x = y 1 + y 1 d x = 1.2 + 1.2 ( 0.2 ) ( ∵ x 1 = x 0 + d x , y 1 = 1.2 and d x = 0.2 ) = 1.2 + 0.24 = 1.44 Thus, the second approximation is 1.44. Evaluate the value of y ( 0.6 ) or third approximation as follows. y 3 = y 2 + f ( x 2 , y 2 ) d x = y 2 + y 2 d x = 1

Thomas' Calculus, Books a la Carte Edition, plus MyLab Math with Pearson eText -- Access Card Package (14th Edition)

14th Edition

ISBN: 9780134768755

Author: Hass

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 9.1, Problem 21E

To determine

The value of y(1) and also to estimate the exact value of y(1) by using Euler method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.1, Problem 20E

Chapter 9.1, Problem 22E

Students have asked these similar questions

Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)

There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three investment? STEP 1: The formula for compound interest is A = nt = P(1 + − − ) n², where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to A = Pert Find r and n for each model, and use these values to write A in terms of t for each case. Annual Model r=0.10 A = Y(t) = 1150 (1.10)* n = 1 Quarterly Model r = 0.10 n = 4 A = Q(t) = 1150(1.025) 4t Continuous Model r=0.10 A = C(t) =…

Use a graphing utility to find the point of intersection, if any, of the graphs of the functions. Round your result to three decimal places. (Enter NONE in any unused answer blanks.) y = 100e0.01x (x, y) = y = 11,250 ×

Chapter 9 Solutions

Thomas' Calculus, Books a la Carte Edition, plus MyLab Math with Pearson eText -- Access Card Package (14th Edition)

Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - In Exercises 1–4, match the differential equations...Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - In Exercises 7–12, write an equivalent first-order...Ch. 9.1 - Prob. 10E

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.