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Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places.) y' = 2xy, y(1) = 1; y(1.5) (explicit solution) y(x) = Xn 1.00 1.10 1.20 1.30 1.40 1.50 xn 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 Yn 1.0000 Yn 1.0000 1.1000 1.2155 1.3492 1.5044 1.6849 1.8955 2.1419 2.4311 2.7715 h = 0.1 Actual Value 1.0000 1.2337 1.5527 1.9937 2.6117 3.4903 h = 0.05 Actual Value 1.0000 1.1079 1.2337 1.3806 1.5527 1.7551 1.9937 2.2762 2.6117 3.0117 3.4903 Absolute Error 0.0000 Absolute Error 0.0000 0.0079 0.0182 0.0314 0.0483 0.0702 0.0982 0.1343 0.1806 0.2402 % Rel. Error 0.00 % Rel. Error 0.00 0.71 1.48 2.27 3.11 4.00 4.93 5.90 6.92 7.98

Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places.) y' = 2xy, y(1) = 1; y(1.5) (explicit solution) y(x) = Xn 1.00 1.10 1.20 1.30 1.40 1.50 xn 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 Yn 1.0000 Yn 1.0000 1.1000 1.2155 1.3492 1.5044 1.6849 1.8955 2.1419 2.4311 2.7715 h = 0.1 Actual Value 1.0000 1.2337 1.5527 1.9937 2.6117 3.4903 h = 0.05 Actual Value 1.0000 1.1079 1.2337 1.3806 1.5527 1.7551 1.9937 2.2762 2.6117 3.0117 3.4903 Absolute Error 0.0000 Absolute Error 0.0000 0.0079 0.0182 0.0314 0.0483 0.0702 0.0982 0.1343 0.1806 0.2402 % Rel. Error 0.00 % Rel. Error 0.00 0.71 1.48 2.27 3.11 4.00 4.93 5.90 6.92 7.98

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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Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places.) y' = 2xy, y(1) = 1; y(1.5) (explicit solution) y(x) = Xn 1.00 1.10 1.20 1.30 1.40 1.50 Xn 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 Yn 1.0000 Yn 1.0000 1.1000 1.2155 1.3492 1.5044 1.6849 1.8955 2.1419 2.4311 2.7715 h = 0.1 Actual Value 1.0000 1.2337 1.5527 1.9937 2.6117 3.4903 h = 0.05 Actual Value 1.0000 1.1079 1.2337 1.3806 1.5527 1.7551 1.9937 2.2762 2.6117 3.0117 3.4903 Absolute Error 0.0000 Absolute Error 0.0000 0.0079 0.0182 0.0314 0.0483 0.0702 0.0982 0.1343 0.1806 0.2402 % Rel. Error 0.00 00000 % Rel. Error 0.00 0.71 1.48 2.27 3.11 4.00 4.93 5.90 6.92 7.98
Transcribed Image Text:Use Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. Find an explicit solution for the initial-value problem and then fill in the following tables. (Round your answers to four decimal places. Percentages may be rounded to two decimal places.) y' = 2xy, y(1) = 1; y(1.5) (explicit solution) y(x) = Xn 1.00 1.10 1.20 1.30 1.40 1.50 Xn 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 Yn 1.0000 Yn 1.0000 1.1000 1.2155 1.3492 1.5044 1.6849 1.8955 2.1419 2.4311 2.7715 h = 0.1 Actual Value 1.0000 1.2337 1.5527 1.9937 2.6117 3.4903 h = 0.05 Actual Value 1.0000 1.1079 1.2337 1.3806 1.5527 1.7551 1.9937 2.2762 2.6117 3.0117 3.4903 Absolute Error 0.0000 Absolute Error 0.0000 0.0079 0.0182 0.0314 0.0483 0.0702 0.0982 0.1343 0.1806 0.2402 % Rel. Error 0.00 00000 % Rel. Error 0.00 0.71 1.48 2.27 3.11 4.00 4.93 5.90 6.92 7.98
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