Thread: Finding differential equation from power series

I have a power series solution to a differential equation and i am trying to find the differential equation that generated it. i guess you would just have to spot it as i can't think of a way of working backwards to the DE?

the series is

y(x)= A + B/X^2 + C/X^4 ....

If it helps that equation is equivalent to Cauchy's equation for refraction of light of varying wavelengths

Is it possible to have some more details?... for example the degree of the [unknown] DE or if it is or not a linear DE?...

Kind regards