# Need help solving Differential Equation

Sin(3x)dx+2ycos(3x)dy=0

So far, I have ∫2ydy=-∫sin(3x)/cos^2(3x)dx. Is that right? If so, how do I integrate sin(3x)/cos^2(3x)?

fresh_42
Mentor
Is this homework? And do you mean ##\sin(3x) + 2\cos(3x) \cdot y(x) \cdot y'(x) = 0\;##?

Is this homework? And do you mean ##\sin(3x) + 2\cos(3x) \cdot y(x) \cdot y'(x) = 0\;##?
These are practice questions for elementary differential equations. Oh...I just realized that there was a typo.

It's: Sin(3x)dx+2yCos^2(3x)dy=0

Again,

So far, I have ∫2ydy=-∫sin(3x)/cos^2(3x)dx. Is that right? If so, how do I integrate -∫sin(3x)/cos^2(3x)?

fresh_42
Mentor
O.k. but please use our homework section for this kind of questions in the future. It automatically inserts a template that you should use.
E.g. it includes a paragraph for your own efforts, which shortens the process a lot. (Normally we don't want to give away ready made solutions to students but try to teach them instead.)

Your typo makes the entire equation more difficult, for otherwise it would have been simply the tangent.
You can look up many integrals here: https://de.wikibooks.org/wiki/Forme...timmte_Integrale_trigonometrischer_Funktionen
It's the wrong language but there is little beside a list of formulas. You won't need the language.
##\int \frac{\sin (3x)}{\cos^2 (3x)} = \frac{1}{3 \cos(3x)}## but I haven't checked whether it's correct.

O.k. but please use our homework section for this kind of questions in the future. It automatically inserts a template that you should use.
E.g. it includes a paragraph for your own efforts, which shortens the process a lot. (Normally we don't want to give away ready made solutions to students but try to teach them instead.)

Your typo makes the entire equation more difficult, for otherwise it would have been simply the tangent.
You can look up many integrals here: https://de.wikibooks.org/wiki/Forme...timmte_Integrale_trigonometrischer_Funktionen
It's the wrong language but there is little beside a list of formulas. You won't need the language.
##\int \frac{\sin (3x)}{\cos^2 (3x)} = \frac{1}{3 \cos(3x)}## but I haven't checked whether it's correct.
Thank you for the link. It translates automatically into any language so it's ok. I wanted to know the whole steps on how to solve the integral: sin(3x)/cos^2(3x) (I found the template, but don't know how to use it yet. I don't go on that much on these forums for help. It's my first time using this to ask for help)

fresh_42
Mentor
Thank you for the link. It translates automatically into any language so it's ok. I wanted to know the whole steps on how to solve the integral: sin(3x)/cos^2(3x) (I found the template, but don't know how to use it yet. I don't go on that much on these forums for help. It's my first time using this to ask for help)
No problem. Knowing the answer one could simply differentiate. The other way might be using one of the forms ##\frac{\sin x}{\cos^2 x}=\frac{\tan x}{\cos x} ## and integrate by parts: ##\int u'v = uv - \int uv'##.

And thanks for the language test. I didn't know this, but surely good to know as - you might have recognized it - there are a lot more formulas for all kind of integrals.

Look up Weierstrass substitution.

• fresh_42
No problem. Knowing the answer one could simply differentiate. The other way might be using one of the forms ##\frac{\sin x}{\cos^2 x}=\frac{\tan x}{\cos x} ## and integrate by parts: ##\int u'v = uv - \int uv'##.

And thanks for the language test. I didn't know this, but surely good to know as - you might have recognized it - there are a lot more formulas for all kind of integrals.
Thanks, I know how to do it now. 