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Consider the ODE y' + tan(ax)y = sin(ax), where a is a nonzero real number. 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?

Consider the ODE y' + tan(ax)y = sin(ax), where a is a nonzero real number. 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?

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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I'm having a hard time finding an integrating factor without using an exponential. How do I find an integrating factor using a trig function? Please, I've asked this question many times and people keep solving it using the regular I.F. = e^∫p(x)dx and this is NOT what I need.

(a) Consider the ODE y' + tan(ax)y = sin(ax), where a is a nonzero real number. 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?
Transcribed Image Text:(a) Consider the ODE y' + tan(ax)y = sin(ax), where a is a nonzero real number. 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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