I have a very simple question )= , but I never understood how to make changes of variables in a differential equation and why! I want to see also a proof but let´s start with an example, let the ODE: $ y^{\left( 2 \right)} + \frac{1} {{x^4 }}y = 0 $
where $ y^{\left( 2 \right)} = \frac{d} {{dx}}\left( {\frac{{dy}} {{dx}}} \right) $
clearly I assuming that y it´s a function that depends on x. Let´s do the change of variable 1/x = s , what will be the new equation? and how can i compute it?