
Differential Equations Ordinary and Partial Differential Equations Math Forum 
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August 10th, 2019, 09:48 PM  #1 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 236 Thanks: 2  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. 
August 10th, 2019, 10:57 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
Your title describes the equation incorrectly. Multiply the equation by 3cos(x²), then you can integrate to get solution (B). 
August 10th, 2019, 11:12 PM  #3 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 236 Thanks: 2 
Hi, Yes, later I understood it's not Linear D.E. It is a Nonexact 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. 
August 10th, 2019, 11:28 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
As you know, it's a nonlinear ODE of first order and first degree, and is nonexact. I found an integrating factor by inspection. 
August 10th, 2019, 11:31 PM  #5 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 236 Thanks: 2 
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. 
August 10th, 2019, 11:59 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
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. 
August 11th, 2019, 12:12 AM  #7 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 236 Thanks: 2 
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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degree, linear, ode, order, solve 
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