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Study23
 2 years ago
Solve the differentiable equation: dy/dx = y^2 ?
Study23
 2 years ago
Solve the differentiable equation: dy/dx = y^2 ?

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terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.2You mean separable, right? :D

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

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.2@Study23 Shall we? :)

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.2Okay, 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?

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

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.2Not 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?

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.2Correct :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

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

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.2Okay, 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 \(n\ne 1\)

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

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1So, I get \(\ \Huge y^1 + C_1 = x \) ?

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1That should be \(\ y^{1} \)

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

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.2If 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 \[\huge y = \frac1{x+C_0}\]

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.2But on the whole, good job :)

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1So, my textbook has this interns of Y= ...

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.2Waaaay ahead of you ^

terenzreignz
 2 years ago
Best ResponseYou've already chosen the best response.2It just needs some algebraic manipulation is all.

Study23
 2 years ago
Best ResponseYou've already chosen the best response.1Oh, 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?

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

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