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terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
You mean separable, right? :D
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
and lol, @openstudy11 It is unfortunately not that simple :D
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
@Study23 Shall we? :)
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Okay, thing about separable differential equations... they are.... separable! LOL Yeah, I know, big surprise :) What I mean is that you can rearrange them so that you can separate them into expressions involving only y and involving only x. Let's have a look at this \[\huge \frac{dy}{dx} = y^2\] You can treat the dy and dx as variables like any other, when separating. Just you try multiplying both sides by dx, and what do you get?
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.1
dy = y^2 dx; I was doing this but I got confused because you couldn't integrate this could you?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Not yet. Now, you could bring all expressions involving y, to the appropriate side of the equation (namely, the side with the dy) You could do this by multiplying \(\large y^{2}\) or \(\Large \frac1{y^2}\) on both sides, and what would you get then?
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.1
dy/y^2=dx (?)
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Correct :D \[\huge \frac{dy}{y^2}=dx\] Now, slip a \(\Huge \int\) sign on both sides of the equation~ and be done with it :D
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.1
So, lny^2=x ?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
oh... \[\huge \int \frac{1}{y^2}dy \ = \int dx\] Are you sure? Maybe this ought to refresh you \[\huge \int y^{2}dy \ = \int dx\]
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Okay, we started with this, right \[\huge \frac{dy}{y^2}=dx\] And we simply integrated both sides \[\huge\color{blue}\int \frac{dy}{y^2}=\color{blue}{\int}dx\] And yes.... \[\huge \int ax^n=\frac{x^{n+1}}{n+1} \] when \(n\ne 1\)
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Sorry, my bad \[\huge \int ax^n = \frac{ax^{n+1}}{n+1}\]
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.1
So, I get \(\ \Huge y^1 + C_1 = x \) ?
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.1
That should be \(\ y^{1} \)
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Mother of sizes... o.O LOL \[\huge y^{1}+C = x\]
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
If you want it as a function of y, you can bring the constant to the other side \[\huge \frac1y=x+C_0\] and then isolate \[\huge y = \frac1{x+C_0}\]
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
But on the whole, good job :)
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.1
So, my textbook has this interns of Y= ...
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Waaaay ahead of you ^
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.1
In terms (autocorrect)
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
Already done... ^
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
It just needs some algebraic manipulation is all.
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.1
Oh, haha I didn't see that! :D. Thanks for all your help @terenzreignz ! I appreciate your encouragement! By the way, any tips for the AP Calc BC exam by the way?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.2
I don't know what exam that is... better consult someone more familiar with it :)
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.1
Oh haha okay. Thanks!
 one year ago

vickky Group TitleBest ResponseYou've already chosen the best response.0
dy/dx=y^2 dy/y^2=dx then integrate both the side 1/y=x+c
 one year ago
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