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August 10th, 2019, 09:48 PM   #1
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Solve the Linear ODE of first order first degree

Hi all,

I'm stuck with this problem. Please help me to identify which method to use.

Attaching the question.

Thanks a lot for your help.
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File Type: jpg 1st order&degree ODE.jpg (25.7 KB, 5 views)
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August 10th, 2019, 10:57 PM   #2
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Your title describes the equation incorrectly.

Multiply the equation by 3cos(x²), then you can integrate to get solution (B).
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August 10th, 2019, 11:12 PM   #3
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Hi,

Yes, later I understood it's not Linear D.E. It is a Non-exact D.E.

Can you tell me how did you come up with the integrating factor ?

Please help me to classify the type of ODE!

Thank you.
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August 10th, 2019, 11:28 PM   #4
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As you know, it's a non-linear ODE of first order and first degree, and is non-exact.

I found an integrating factor by inspection.
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August 10th, 2019, 11:31 PM   #5
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Understood. Thanks for the help.

I have problem in solving/integrating trig functions. Can you let me know any books to refer to improve myself?

Thanks in advance.
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August 10th, 2019, 11:59 PM   #6
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Any book on trigonometry will help to some extent by making you more familiar with trigonometric functions.

Unfortunately, integration in general (not just where trigonometric functions are involved) uses a wide variety of techniques and can be tricky. I don't know of a textbook that deals with integration of trigonometric functions in detail. However, you would probably find it useful to read various worked examples that can be found online.
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August 11th, 2019, 12:12 AM   #7
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Thanks a ton for your help.

I solved it. I will work on more problems to get familiarized with different sorts.

Have a nice day
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