# Math Help - existance of a specific diff. eq.

1. ## existance of a specific diff. eq.

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...

2. anyone?

3. 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: $2y y"+ 2 y'^2= 2$.