Consider the solution of the differential equation y=-3y passing through y(0) = 1. Sketch the slope field for this differential equation, and sketch the solution passing through the point (0,1). Use Euler's method with step size h = 0.2 to estimate the solution at x = 0.2, 0.4, . . . , 1, using these to fill in the following table. Note: Be sure not to round your answers at each step! x = 0 0.4 y≈ 1 -1.44 0.2 O A. over 9. 9- 0.6 B. under Check that y = e-3 is a solution to y = -3y with y(0) = 1. 0.8 help (numbers) Plot your estimated solution on your slope field. Compare the solution and the slope field. Is the estimated solution an over or under estimate for the actual solution? 1.0
Consider the solution of the differential equation y=-3y passing through y(0) = 1. Sketch the slope field for this differential equation, and sketch the solution passing through the point (0,1). Use Euler's method with step size h = 0.2 to estimate the solution at x = 0.2, 0.4, . . . , 1, using these to fill in the following table. Note: Be sure not to round your answers at each step! x = 0 0.4 y≈ 1 -1.44 0.2 O A. over 9. 9- 0.6 B. under Check that y = e-3 is a solution to y = -3y with y(0) = 1. 0.8 help (numbers) Plot your estimated solution on your slope field. Compare the solution and the slope field. Is the estimated solution an over or under estimate for the actual solution? 1.0
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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Question
Ordinary Diff Equations
Transcribed Image Text:Consider the solution of the differential equation y' = −3y passing through y(0) = 1.
Sketch the slope field for this differential equation, and sketch the solution passing through the point (0,1).
-
Use Euler's method with step size h 0.2 to estimate the solution at x =
Note: Be sure not to round your answers at each step!
0.2
0.4
x = 0
y≈ 1 -1.44
O A. over
● B. under
Check that ye -3x
0.2, 0.4,
is a solution to y'= -3y with y(0) = 1.
0.6
‚ 1, using these to fill in the following table.
... 9
help (numbers)
Plot your estimated solution on your slope field. Compare the solution and the slope field. Is the estimated solution an over or under estimate for the actual
solution?
0.8
1.0
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