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Find the exact solution of the given initial value problem, then apply Euler's method

Find the exact solution of the given initial value problem, then apply Euler's method

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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Find the exact solution of the given initial value problem, then apply Euler's method. Q. no. 12 only
A programmable calculator or a computer will be useful for Problems 11 through 16. In each problem find the exact so- lution of the given initial value problem. Then apply Euler's method twice to approximate (to four decimal places) this so- lution on the given interval, first with step size h = 0.01, then with step size h = 0.005. Make a table showing the approxi- mate values and the actual value, together with the percentage error in the more accurate approximation, for x an integral multiple of 0.2. Throughout, primes denote derivatives with respect to x. 11. y' = y – 2, y(0) = 1;0 S x SI 12. y' = }v – 1)², y(0) = 2;0 < x S 1 13. yy' = 2x³, y(1) = 3; 1 < x < 2 14. xy' = y², y(1) = 1; 1 < x < 2 15. xy' = 3x – 2y, y(2) = 3; 2 < x<3 16. y²y' = 2x$, y(2) = 3;2 < x S 3
Transcribed Image Text:A programmable calculator or a computer will be useful for Problems 11 through 16. In each problem find the exact so- lution of the given initial value problem. Then apply Euler's method twice to approximate (to four decimal places) this so- lution on the given interval, first with step size h = 0.01, then with step size h = 0.005. Make a table showing the approxi- mate values and the actual value, together with the percentage error in the more accurate approximation, for x an integral multiple of 0.2. Throughout, primes denote derivatives with respect to x. 11. y' = y – 2, y(0) = 1;0 S x SI 12. y' = }v – 1)², y(0) = 2;0 < x S 1 13. yy' = 2x³, y(1) = 3; 1 < x < 2 14. xy' = y², y(1) = 1; 1 < x < 2 15. xy' = 3x – 2y, y(2) = 3; 2 < x<3 16. y²y' = 2x$, y(2) = 3;2 < x S 3
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