Differentail Eq. For circle passing through origin

[Isma]

can some 1 help me with it pleasezz

 

[quantumdude]

can u post the qstn pleasezz?

 

[Isma]

question is find the differential eq. for circle that passes through origin.

 

[quantumdude]

That can't be all there is to it. There are an infinite number of circles that pass through the origin.

 

[Isma]

exactly...i m v confused...thats all wat the question is for assignment i ve to submit tomorrow
i just kno the answer but don't kno anything else
ans: 2ay''+y'(raise to the power 3)=0

 

[vaishakh]

2ay + y^3 = 0.
2a = -y^2
This represents a circle!

 

[Isma]

yesss!
thx a lot :)

 

[Isma]

but how will we come to this eq. from start if we dint know the DE?

 

[ziad1985]

what is the eq you were given for circle that pass in (0,0) ? is it like this one : $$(x-a)^2 +(y-b)^2 = a^2 +b^2$$

 

[HallsofIvy]

How about writing out the entire problem as it was given?

just kno the answer but don't kno anything else
ans: 2ay''+y'(raise to the power 3)=0

How can that be an answer when there was no "a" in the original question?

2ay + y^3 = 0.
2a = -y^2
This represents a circle!

In what sense does that represent a circle?

yesss!
thx a lot :)

Did you understand what he meant??

Any circle, that passes through the origin can be written
(x- a)²+ (y- b)²= a²+ b²
(I just noticed that ziad1985 said that!)

Differentiating wrt x, 2(x-a)+ 2(y-b)y'= 0.

Differentiating again, 2+ 2y'²+ 2(y-b)y"= 0.

Now combine those into an equation that does not have either a or b in it.

 

[Isma]

actually...this assignment was given just after 1st lecture on DE in class...so i was v much messed up in mind...nd abt that thanks heheheh...it made sense at that moment but not in the next 1:)
i really appreciate u helpin me ...i m going to solve it like that
thx!