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n 0 1 2 Suppose that we use Euler's method to approximate the solution to the differential equation 24 In+1 = In th, Complete the following table. Your answers should be accurate to at least seven decimal places. In 0.5 3 4 Let f(x, y) = x/y. We let o 0.5 and 30 = 8 and pick a step size h = 0.2. Euler's method is the the following algorithm. From an and Yn, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing 5 Yn 8 dy da y The exact solution can also be found using separation of variables. It is y(x) = Thus the actual value of the function at the point x = 1.5 (1.5) = 1 y(0.5) = 8. Yn+1 Yn+h. f(xn, yn).

n 0 1 2 Suppose that we use Euler's method to approximate the solution to the differential equation 24 In+1 = In th, Complete the following table. Your answers should be accurate to at least seven decimal places. In 0.5 3 4 Let f(x, y) = x/y. We let o 0.5 and 30 = 8 and pick a step size h = 0.2. Euler's method is the the following algorithm. From an and Yn, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing 5 Yn 8 dy da y The exact solution can also be found using separation of variables. It is y(x) = Thus the actual value of the function at the point x = 1.5 (1.5) = 1 y(0.5) = 8. Yn+1 Yn+h. f(xn, yn).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that we use Euler's method to approximate the solution to the differential equation x² ==; n 0 1 Let f(x, y) = x/y. We let = 0.5 and yo = 8 and pick a step size h = 0.2. Euler's method is the the following algorithm. From , and yn, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing In+1 = n + h, Complete the following table. Your answers should be accurate to at least seven decimal places. In 0.5 2 3 4 5 Yn 8 dy dx Y The exact solution can also be found using separation of variables. It is y(x) = Thus the actual value of the function at the point x = 1.5 y(1.5) = y(0.5) = 8. Yn+1 Yn+h. f(xn, yn).
Transcribed Image Text:Suppose that we use Euler's method to approximate the solution to the differential equation x² ==; n 0 1 Let f(x, y) = x/y. We let = 0.5 and yo = 8 and pick a step size h = 0.2. Euler's method is the the following algorithm. From , and yn, our approximations to the solution of the differential equation at the nth stage, we find the next stage by computing In+1 = n + h, Complete the following table. Your answers should be accurate to at least seven decimal places. In 0.5 2 3 4 5 Yn 8 dy dx Y The exact solution can also be found using separation of variables. It is y(x) = Thus the actual value of the function at the point x = 1.5 y(1.5) = y(0.5) = 8. Yn+1 Yn+h. f(xn, yn).
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