Computer Numerics Consider the linear DEs in Problem, with y(0) = 1.
(a) Use a computer package with different numerical methods to find y(1).
(b) Use the exact solution (as found in the corresponding Problems 42, 43 and 47) to compute y(1) and compare with your approximations.
(c) Summarize what happens with different methods and different step sizes.
(d) Tell which approximations are misleading and why.
y′ + 2ty = 1
Computer Visuals For the linear DEs in Problem:
(a) Use an open-ended graphical DE solver to draw a direction field and some solutions.
(b) Find the exact solution and relate it to your picture in (a).
(c) If there is a steady-state solution, add it to your picture in (a) and highlight it in color. Then identify the transient and steady-state parts of the general solution in (b).
Problem 42
y′ + 2y= t
Problem 43
y′ − y= e3t
Problem 47
y′ + 2ty = 1
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