Solve the Linear ODE of first order first degree

Nov 2015
242
4
hyderabad
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.
 

Attachments

skipjack

Forum Staff
Dec 2006
21,379
2,410
Your title describes the equation incorrectly.

Multiply the equation by 3cos(x²), then you can integrate to get solution (B).
 
Nov 2015
242
4
hyderabad
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.
 

skipjack

Forum Staff
Dec 2006
21,379
2,410
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.
 
Nov 2015
242
4
hyderabad
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.
 

skipjack

Forum Staff
Dec 2006
21,379
2,410
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.
 
Nov 2015
242
4
hyderabad
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:)