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anonymous
 one year ago
Can someone help a novice out?! Differential Equation SOS! Find the DE knowing the final answer y=(xc)^3 Thanks a lot!!!
anonymous
 one year ago
Can someone help a novice out?! Differential Equation SOS! Find the DE knowing the final answer y=(xc)^3 Thanks a lot!!!

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Should I just get rid of the C?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and if so. idk really know how tbh

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but the C remains! shouldn't I come to the point of which I don't have constants?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Loser66 will you be my savior?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1You can find y' by differentiating the y=(xc)^3.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1why can't the differential equation be y'=3(xc)^2 with condition .. let me figure it out... y=(xc)^3+C y(0)=(0c)^3+C y(0)=c^3+C y(0)+c^3=C So why can't the differential equation be y'=3(xc)^2 with condition y(0)=c^3 ?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1y=(xc)^3 y'=3(yc)^2 y"=6(yc) so y=(y"/6)^3 or (y")^3216y=0

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1oh, sorry, I didn't see the condition.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I don't see how these rules in which we find a differential equation posted in the original post. @Loser66

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I don't see that we aren't allowed to use initial conditions or find a nonlinear diff equation.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1it would be nice though if @Hipocampus can settle what we are talking about though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmmm that's all I have...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0idk more than you guys about this question

freckles
 one year ago
Best ResponseYou've already chosen the best response.1So the solution can be nonlinear or can have conditions ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0as long as the C is gone

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2@freckles You see, @mathmate derives to another way, we have another ODE. I have a bunch of ODE satisfy the given information. YOu add more condition to get another one. That is the reason why it is invalid!! We know that the solution of ODE is UNIQUE for a specific condition. Unfortunately, we didn't have it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can I ask another question then?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2close this and open a new one, please.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2@ganeshie8 @dan815 @oldrin.bataku @SithsAndGiggles @Hipocampus That is the reason why I don't want you to mix this question with the other one

freckles
 one year ago
Best ResponseYou've already chosen the best response.1Oh so no conditions allowed you are saying @Loser66

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2@freckles I didn't say "no conditions allowed", just don't use the ungiven conditions.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you want to find a differential equation subject to no conditions is what you are looking for the rest are valid though if you provide conditions in which I have

freckles
 one year ago
Best ResponseYou've already chosen the best response.1you get to make up the differential equation, why can't you make up the conditions that it is subject to?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and I'm not really making it up I'm based my condition off what the solution should be.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.2Anyway!! I think if we make up a condition and have a Unique solution for that condition, we are ok :)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2aren't we looking for the differential equation of order 1, whose general solution is the set of standard cubics translated horizontally ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I don't know it wasn't specify that had to have order 1

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2the order has to be 1 because there is only 1 arbitrary constant in the given general solution

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2number of arbitrary constants and the order of de must agree, right

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well I was thinking that this would be okay: \[y'=3(xc)^2 \text{ with condition } y(0)=c^3 \] but are you saying we are suppose to be treating the c from y=(xc)^3 has like the constant of integration

freckles
 one year ago
Best ResponseYou've already chosen the best response.1meant to end that with a ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2this should work \[(y')^3 = 27y^2\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I like that requires no conditions

freckles
 one year ago
Best ResponseYou've already chosen the best response.1but I still think my way is valid

freckles
 one year ago
Best ResponseYou've already chosen the best response.1only because there was not much put into the "rules" of finding the differential equation

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Haha true, they should have asked it less ambiguously: eliminate the arbitrary constant to get the differential equation that represents the family of standard cubics translated horizontally

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you could just do: $$y=(xc)^3\\y^{1/3}=xc\\\frac13 y^{2/3}y'=1\\y'=3y^{2/3}$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the solutions are the oneparameter family of monic cubics up to horizontal translation \(y=(xc)^3\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops, that should read \(\frac13 y^{2/3}y'=1\implies y'=3y^{2/3}\) but same point
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