Solve equations in two variables


I have these equations

$
L = 3 Big ( frac { dot a ^ 2} {a ^ 2} + frac { dot a dot b} {ab} big) – frac {1} {a ^ 3} \ L = Big (2 frac { ddot a ^ 2} {a} + frac { dot a ^ 2} {a ^ 2} + frac { ddot b ^ 2} {b} + 2 frac { dot a dot b} {ab} big)
\ L = – Big (2 frac { dot a ^ 2} {a ^ 2} + 2 frac { dot a dot b} {ab} + frac { ddot a} {a} + frac { ddot b} {b} Big) \
L = 3 b ^ 2 Big ( frac { ddot a} {a} + frac { dot a ^ 2} {a ^ 2} Big) $

How to solve in Mathematica to get $ b $ in terms of $ a $,

I tried something like this

To solve[{3 ((D[a
on
3 b

But of course it did not work because the number of equations is greater than the unknown variables. How do you get b as a function in a?

Any help appreciated!