Calculus help please!

[Wizibirb]

I need to take the integral of this equation, help please.

Cos(x) dy - (y)(Sin(x)) dx = Cos(x) dx

[Knaight]

You are aware of the numerous integral calculators on the internet?

In the mean time, try to get this down to a differential equation. All sorts of stuff is worth trying, dividing both sides by Cos(x) might make a good start (remember that Sin(x)/Cos(x)=Tan(x))

[Wizibirb]

yes I am, however getting just an answer does no good, if this was about finding a simple answer it would already be done.

I want to know how to do it. If you could point me in the direction of a website that had step by step instructions on this integral that would be useful.

[Jack Squat]

cos(x)y +ycos(x)= sin(x) + C I think.

integral of cos(x)dy would be cos(x)y, since cos(x) would act like a constant.
integral of -ysin(x) would be -y (-cos(x)) or ycos(x)
integral of cos(x) is sin(x). All + C of course since it's not definite.

I could be missing something, as I don't remember doing an equation like this before and don't know if anything's weird in regards to doing it. It's been a few years since I've taken Calc.

[Capt Spanner]

I believe you can take the integral of each differential part individually:

y cos(x) -y cos(x) = -sin(x) +C

sin(x) = C

[Wizibirb]

@ Jack Squat - You can not treat cos X as a constant or y for that matter, because they are both dependent on each other.

@ Knaight - I tried that and I ended up with

dy= (1 + ytan(x)) Dx

you still have the problem of the Y and once again it can not be treated as a constant. Unless I am mistaken about x and y being dependent on each other. though last time I checked they are.

[The_JJ]

Integration by parts?

[Sir Enigma]

Does the problem give you any more information? As it stands, assuming y=f(x), I'm not even sure this is solvable - as you've already shown, there's no way to separate the variables, so no standard integration technique will work.

[TSGames]

I need to take the integral of this equation, help please.

Cos(x) dy - (y)(Sin(x)) dx = Cos(x) dx

I'm not very good with Calculus, but this is what I got:

Cos(x) dy - (y)(Sin(x)) dx = Cos(x) dx :://::starting equation
dy - y*Sin(x)dx/Cos(x) = dx :://::divide by Cos(x)
dy - y*Tan(x)dx = dx :://::simplify
dy/dx -y*Tan(x) = 1 :://::divide by dx
dy/dx = 1 + y*Tan(x) :://::add y*Tan(x) to both sides

After this, it would normally be a simple matter of integrating with respect to one variable and then the other, however, the relation between the variables is not specified, so I'm not really sure what you can do with that (lack of)information...

[mcl01]

First divide by dx to get...
cosx * dy/dx - y*sinx = cosx

Use product rule.

d/dx(f(x)*g(x)) = f'(x)*g(x) + f(x)*g'(x)
f(x) = y(x)
g(x) = cosx
f'(x) = dy/dx
g'(x) = -sinx

d/dx(y*cosx) = dy/dx*cosx - y * sinx
Therefore,
d/dx(y*cosx) = cosx

now it's a simple matter of integration on both sides to undo the derivative. You pick up a constant of integration due to the indefinite integral, and now you can simply divide by cosx to solve for y.

[Jack Squat]

@ Jack Squat - You can not treat cos X as a constant or y for that matter, because they are both dependent on each other.

No they aren't, unless there's something special about having it set up as an equation like this. How I'm reading the equation, it's decidedly clear that for cos(x) dy the variable y is the one that has to be integrated. Likewise for -y*sin(x) dx. and x. How I saw the equation was

∫cos(x) dy - ∫ysin(x) dx = ∫cos(x) dx

This would be rewritten as
cos(x)∫dy - y∫sin(x)dx = ∫cos(x) dx
since you don't take the integral of a variable that's not in that part.

...

Of course, now that I look at it a little more, I can see that the left side was derived with the product rule, so we'd be looking at

y*cos(x) + C as the original of that side.

ycos(x) = -sin(x) + C

y=-(sin(x)/cos(x)) + C

y= -tan(x) + C

So forget what I said above. Like I said, it's been a few years :smalltongue:

EDIT: @V thanks. I always tend to make those sorts of mistakes. Good thing I'm not a math major :smalltongue:

[mcl01]

The above solution is mostly correct - cosx is not constant, however, so you can't simply merge it into the constant of integration.

y = tanx + C/cosx

[Bryn]

I'm tired and I don't think I've ever tried to do an equation like this one but I got the same answer as Jack Squat + mcl01 so I guess I did it right anyway :smallamused:

http://img7.imageshack.us/img7/5853/randommathsproblem.png

[Sir Enigma]

*headdesk* How did I miss that? Serves me right for trying to do calculus at 3am...

Just a nitpick, there's a sign error - integral(cosx dx) = sinx, not -sinx, so the correct answer should be y = tanx+C/cosx

EDIT: Ninjas everywhere!

[mcl01]

Ah right - my bad. Silly integrals and derivatives and their reversed signs. :( I'll correct my original post.