# Solve the Linear ODE of first order first degree

#### Lalitha183

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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#### skipjack

Forum Staff
Your title describes the equation incorrectly.

Multiply the equation by 3cos(xÂ²), then you can integrate to get solution (B).

#### Lalitha183

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 ?

Thank you.

#### skipjack

Forum Staff
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.

#### Lalitha183

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?

#### skipjack

Forum Staff
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.

#### Lalitha183

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