(a) Consider the ODE y' + tan(ax)y = sin(ax). Let a = 1, to start, and if you'd like to solve a harder exercise, then solve for other values of a € R. Find an integrating factor without using an exponential, but instead, a trig function. Then solve. If you used the standard method for finding an integratin factor, would anything in your solution have changed? (b) Repeat the steps in part (a) for the ODE y' + cot(ax)y — sin(ax) = 0. (c) Do you see a pattern? Can you come up with another example of a linear ODE that can be solved with an integrating factor found without using the standard formula? If so, does using the standard formula result in the same integrating factor?
(a) Consider the ODE y' + tan(ax)y = sin(ax). Let a = 1, to start, and if you'd like to solve a harder exercise, then solve for other values of a € R. Find an integrating factor without using an exponential, but instead, a trig function. Then solve. If you used the standard method for finding an integratin factor, would anything in your solution have changed? (b) Repeat the steps in part (a) for the ODE y' + cot(ax)y — sin(ax) = 0. (c) Do you see a pattern? Can you come up with another example of a linear ODE that can be solved with an integrating factor found without using the standard formula? If so, does using the standard formula result in the same integrating factor?
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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Transcribed Image Text:(a) Consider the ODE y' + tan(ax)y = sin(ax). Let a = 1, to start, and if you'd like to solve
a harder exercise, then solve for other values of a € R. Find an integrating factor without
using an exponential, but instead, a trig function. Then solve. If you used the standard
method for finding an integratin factor, would anything in your solution have changed?
(b) Repeat the steps in part (a) for the ODE y' + cot(ax)y — sin(ax) = 0.
(c) Do you see a pattern? Can you come up with another example of a linear ODE that can
be solved with an integrating factor found without using the standard formula? If so,
does using the standard formula result in the same integrating factor?
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