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Dividing differential equations

  • Thread starter Hybird
  • Start date
  • #1
26
0

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: [tex]\frac{d^{2}X}{da^{2}}[/tex] = Some polynomial

and,

eqn2: [tex]\frac{d^{2}T}{da^{2}}[/tex] = 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).
 

Answers and Replies

  • #2
26
0
Ok, maybe I should give the RHS of the equations too..


eqn1: [tex]\frac{d^{2}X}{da^{2}}[/tex] = -X [tex]\frac{dT}{da}}[/tex] [tex]\frac{dT}{da}}[/tex]

eqn2: [tex]\frac{d^{2}T}{da^{2}}[/tex] = [tex]\frac{-2}{X^{2}}[/tex] [tex]\frac{dX}{da}}[/tex] [tex]\frac{dT}{da}}[/tex]
 
  • #3
26
0
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))
 

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