Question

integrate(-2cos(x)/[y*sin(x)])dx

Answer 1

is that part of a double integral ? whats `y` doing in the denominator ?

Answer 2

it's not a double integral, this integral came out as a intermediate step in solving a differential integral

Answer 3

I'm not sure how to treat the y in the denominator. I was thinking of treating it as a constant?

Answer 4

solving a differential equation*, not differential integral* typo

Answer 5

thats not allowed then
whats the original differential equation ?

Answer 6

yeah you have to completely separate variables before integrating

Answer 7

\[\frac{ 3y ^{2}\cot(x)+\sin(x)\cos(x) }{ 2y } = \frac{ dy }{ dx }\]

Answer 8

looks like a bernoulli equation

http://tutorial.math.lamar.edu/Classes/DE/Bernoulli.aspx

Answer 9

Oh it does look like a bernoulli equation. We haven't covered it in class yet but I have seen it on the course outline.

Answer 10

oh ok, well there may be another way , what are you covering right now?

Answer 11

1. Direct Integration
2. Substitution --> Integration
3. Exact Equations
4. Made Exact - Integrating Factor
5. First Order Linear Fomula
6. Linearlize --> Use formula

Answer 12

you are going to make a substitution to change it to a Linear DE
Bernoulli is just a nice general form to help tell you exactly what substitution to make
not sure what your teacher wants exactly, prob covered in topic 5 and 6 i guess

Answer 13

substitution is:
v = y^2
v' = 2y y'

just say you skipped to bernoulli section haha

Answer 14

haha thanks, I'll try it

Answer 15

Just a quick question though about the two variable integral i mentioned earlier;

Answer 16

so you can't integrate when there is x and y in the function if it's just integrating by dx, but I know from other calc courses that if it's a double integral,

Answer 17

you can integrate with respect to dxdy and treat one of the variables constant as you integrate.

Answer 18

So you can't apply this procedure of keeping variables constant in the integral i mentioned above?

Answer 19

sorry about reply being broken up^ the post button didnt' work when it was all together ..

Answer 20

hmm well to use a double integral you need dxdy to be a product on same side
that usually doesn't work out in most DE

Answer 21

how do you turn dy/dx into dy*dx ?

Answer 22

also with a double integral you need limits

Answer 23

can u send the Q which is given and you have to solve

Answer 24

The original ODE problem is: \[\frac{ 3y ^{2}\cot(x)+\sin(x)\cos(x) }{ 2y }\]
But I solved it, thanks