existance of a specific diff. eq.

**vonflex1** · February 4th 2010, 02:40 PM

hi,

i have the following question:

is there an ordinary 2nd order, linear differential equation,

which solution is the family of circles:

$(x-c1)^2+y^2 = c2^2$ ?

and if there is, find such an example.

i am clueless...

**vonflex1** · February 5th 2010, 10:53 AM

anyone?

**HallsofIvy** · February 6th 2010, 05:34 AM

Originally Posted by vonflex1

hi,

i have the following question:

is there an ordinary 2nd order, linear differential equation,

which solution is the family of circles:

$(x-c1)^2+y^2 = c2^2$ ?

and if there is, find such an example.

i am clueless...

Differentiate the given equation with respect to x. $2(x- c_1)+ 2y y'= 0$ . Write that as $2y y'= 2x- 3c_1$ and differentiate again: $2y y"+ 2 y'^2= 2$ .

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