Dividing differential equations

[Hybird]

Homework Statement

This is more of a problem I have with my knowledge of differentials. I have two second order differential equations for variables X(a) and T(a). I want to get an expression for X(T). I know I have to divide them, but how do you go about dividing them if they are explicitly stated as:

eqn1: \frac{d^{2}X}{da^{2}} = Some polynomial

and,

eqn2: \frac{d^{2}T}{da^{2}} = Some polynomial

The Attempt at a Solution

I know for first derivative with respect to 'a', you can just divide them directly and the 'da' part will just cancel, but what would you get for a second derivative?

Example of first derivative would be:

dX/da divided by dT/da would equal dX/dT, and you could just solve the resulting simple differential equation to get X(T).

 

[Hybird]

Ok, maybe I should give the RHS of the equations too..


eqn1: \frac{d^{2}X}{da^{2}} = -X \frac{dT}{da}} \frac{dT}{da}}

eqn2: \frac{d^{2}T}{da^{2}} = \frac{-2}{X^{2}} \frac{dX}{da}} \frac{dT}{da}}

 

[Hybird]

Never mind, I'm retarded. I just expressed the second order derivative as :

d/da(dX/da) and when you divide it by d/da(dT/da) the d/da part cancels because its just like an operator. I got an exponential result as X(T) = exp(T/sqrt(2))