AP Calculus Help

[Cat 290]

Well, since there's no "off-topic" section, thought I'd post this here. I'm currently stuck on a calculus problem, one that was on my midterm that I missed and I'm trying to fix it and study from it. It's a differential equation, so here it is.

 

dy         -xy

---   =   ------

dx         ln (why)

 

Ln(why) is the natural log of why, just for clarification purposes. Anyways, I need to find the general solution of the differential equation, and then I need to find the solution that satisfies the condition that why= e^2 when x=0. 

 

Here are the steps I did:

 

Multiplied dx and ln(why) out to both sides, and then divided by why so I then got:

 

(ln(why) dy) / why = -xdx

 

I then integrated both sides, to get:

 

Indefinite integral of ln(why) / why dy = indefinite integral of -xdx

 

Which then turns into ln^2(why)/2 = -x^2/2

 

Multiplying out the two gives you ln^2(why) = -x^2

 

Since you have a square on either side, you can square root it, no?

 

So then you get ln(why) = sqrt(-x^2). 

 

Which then turns into why = e^sqrt(-x^2) + C. 

 

Can anybody double check me here and make sure I'm doing this right? I thin I'm missing a step somewhere....

 

 

EDIT: Lossy you stupid idiot and your stupid filters, ruin all my math problems. D:<

[Darmuh 1090]

this probably isn't the best place for math help

[BosnianArmy 517]

Well good luck with that, ain't nobody got time for dat :dave:

[siikdude 240]

best bet is too ask reddi. Over here you I don't think you'll get answers

[Sentrex 785]

Not even going to bother reading it until someone removes that stupid yy filter

[Zack 100]

a^{2 +} b^{2 =} c²

 

 

ezpz

[Thomas 179]

Answer: y(x) = c_1 e^(Ei(2 log(x)))

[siikdude 240]

Here I am in algebra 1 huehuehue

[zander ◔◡◔ 125]

Multiplying out the two gives you ln^2(why) = -x^2

 

Since you have a square on either side, you can square root it, no?

 

So then you get ln(why) = sqrt(-x^2). 

 

You can't square root a negative number.

Instead, add the constant in earlier to make it  ln(why) = sqrt(c - x^2)

This gives you why = e^sqrt(c - x^2)

Substituting in why = e^2 and x = 0, c = 4

So your final answer should be why = e^sqrt(4-x^2)

 

Edit: Just saw the date; sorry for bumping this thread.

[Cat 290]

You can't square root a negative number.

Instead, add the constant in earlier to make it  ln(why) = sqrt(c - x^2)

This gives you why = e^sqrt(c - x^2)

Substituting in why = e^2 and x = 0, c = 4

So your final answer should be why = e^sqrt(4-x^2)

 

Edit: Just saw the date; sorry for bumping this thread.

Heh, I actually figured it out later that night and was too lazy to update the post. You were correct though, if I remember correctly. 

[BosnianArmy 517]

Americans way of math... :dave:...

 

*EDIT*

 

Didn't know algebra is from Arabia? :o..

 

In place to use numbers you guys are using letters, that's just dumb for me to look at that way. Just use simply 5*5= 25 lol

[zander ◔◡◔ 125]

Americans way of math... :dave:...

 

*EDIT*

 

Didn't know algebra is from Arabia? :o..

 

In place to use numbers you guys are using letters, that's just dumb for me to look at that way. Just use simply 5*5= 25 lol

 

What are you even talking about?

[Sentrex 785]

Americans way of math... :dave:...

 

*EDIT*

 

Didn't know algebra is from Arabia? :o..

 

In place to use numbers you guys are using letters, that's just dumb for me to look at that way. Just use simply 5*5= 25 lol

:facepalm:

Say you've been given the area of a rectangle and one of the sides, but you want to know what the other side is. You can't just plug in numbers since you don't know what they are.

You can use algebra to find this out easily. You know the first side is 7cm and the area is 21cm. By using x to stand in for the other side it becomes a lot easier to solve.

7 * x = 21

x = 21/7

x = 3

Granted that this is very simple and can be done by pretty anyone in their head, but this is the simplest form of algebra I could think of.

With more complex questions it become pretty much impossible to solve without the use of algebra.

[Spencer 87]

Here I am in algebra 1 huehuehue

I'm on the same page as you man, that shit looks confusing..

[BosnianArmy 517]

:facepalm:

Say you've been given the area of a rectangle and one of the sides, but you want to know what the other side is. You can't just plug in numbers since you don't know what they are.

You can use algebra to find this out easily. You know the first side is 7cm and the area is 21cm. By using x to stand in for the other side it becomes a lot easier to solve.

7 * x = 21

x = 21/7

x = 3

Granted that this is very simple and can be done by pretty anyone in their head, but this is the simplest form of algebra I could think of.

With more complex questions it become pretty much impossible to solve without the use of algebra.

 

We got other ways to do it :dave:

 

You can look trough here http://www.fisme.science.uu.nl/staff/marjah/documents/TOURdef+ref.pdf

 

Anyways, every country got a little bit different ways

[zander ◔◡◔ 125]

We got other ways to do it :dave:

 

You can look trough here http://www.fisme.science.uu.nl/staff/marjah/documents/TOURdef+ref.pdf

 

Anyways, every country got a little bit different ways

 

That pdf outlines the maths curriculum for primary school children :|

 

 

 

The 'syntax', if you will, of maths is the same regardless of country. If you've never come across algebra, then I question your age.

 

/sorryforbeingmeannooffense

[BosnianArmy 517]

That pdf outlines the maths curriculum for primary school children :|

 

 

 

The 'syntax', if you will, of maths is the same regardless of country. If you've never come across algebra, then I question your age.

 

/sorryforbeingmeannooffense

 

Not everyone is using algebra keep that in mind. Some people are using different math ways.

[zander ◔◡◔ 125]

This isn't worth it.

[Sentrex 785]

This isn't worth it.

Welcome to the club of anyone who's disagreed with Bosnian

[Tinman 427]

Just asked two Dutch fwends of mine whether or not they study/use algebra in their mathematics syllabus... they of course answered yes.

 

Looks like it's time for you to find another school/college if you are even at one (by the looks of things, you're not :/ )

[iMtroll 1084]

They teach algebra anywhere that teaches basic maths Bosnian...

 

So as Tinman said, if you are in a school/college, you may want to find a new one.

 

 

ANYWAY, let's not cause an argument in this topic. 

[BosnianArmy 517]

LMFAO
 
I just did a research from a dutch algebra and I do that as well.... but since we do not use letters (atleast our level)  we do it on a other way likethis:

four-square
carrot
fractures
volume/ content

etc etc

 

One example:

 

A classroom is 6,20 meters wide and 6,80 meters large. According to the law, the students needs atleast 1,3 m² per person.

 

What's the maximum for the amount of students?

[atrX 426]

Didn't you study ICT, Bosnian? How did you not get kicked out yet if you don't even know basic algebra? o_O

[Sentrex 785]

A classroom is 6,20 meters wide and 6,80 meters large. According to the law, the students needs atleast 1,3 m² per person.

 

What's the maximum for the amount of students?

Sorry not trying to be mean but, what age group is this meant for?

[BosnianArmy 517]

Sorry not trying to be mean but, what age group is this meant for?

 

It was just a example -.-...

 

And if I am gonna put a better example here, I'm not from some high university or some big ass math student to do some big math stuff. Actually we are just doing litteraly basic things. Anyways it ends here.