Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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
See similar textbooks
icon
Related questions
Question

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?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS