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(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?

(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?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.7: Applied Problems
Problem 68E
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Please first find the integrating factor using trig function and NOT an exponential.

(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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