Let y(t) be the solution to y = 5te^(-y) satisfying y(0) = -3 a) use euler method with time step h = 0.2 to approximate y(0.2), y(0.4),.....y(1.0) (k ,tk ,y(k))-----*legend/format for the problem* 0,0,-3 1, 0.2, ? 2, 0.4, ? 3, 0.6, ? 4, 0.8, ? 5, 1 , ? use separation of variables to find y(t) exactly y(t) = ? Compute the error in the approximations to y(0.2), y(0.6) and y(1) absolute value (y(0.2) - y1) = ? absolute value (y(0.6) - y3) = ? absolute value (y(1) - y5) = ?
Let y(t) be the solution to y = 5te^(-y) satisfying y(0) = -3 a) use euler method with time step h = 0.2 to approximate y(0.2), y(0.4),.....y(1.0) (k ,tk ,y(k))-----*legend/format for the problem* 0,0,-3 1, 0.2, ? 2, 0.4, ? 3, 0.6, ? 4, 0.8, ? 5, 1 , ? use separation of variables to find y(t) exactly y(t) = ? Compute the error in the approximations to y(0.2), y(0.6) and y(1) absolute value (y(0.2) - y1) = ? absolute value (y(0.6) - y3) = ? absolute value (y(1) - y5) = ?
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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Let y(t) be the solution to y = 5te^(-y) satisfying y(0) = -3
a) use euler method with time step h = 0.2 to approximate y(0.2), y(0.4),.....y(1.0)
(k ,tk ,y(k))-----*legend/format for the problem*
0,0,-3
1, 0.2, ?
2, 0.4, ?
3, 0.6, ?
4, 0.8, ?
5, 1 , ?
use separation of variables to find y(t) exactly
y(t) = ?
Compute the error in the approximations to y(0.2), y(0.6) and y(1)
absolute value (y(0.2) - y1) = ?
absolute value (y(0.6) - y3) = ?
absolute value (y(1) - y5) = ?
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