Hi jescavez

We have the equation and we want to replace and by so we need to compute and in terms of and . Let's start with :

The chain rule states that hence

Let's differentiate a second time with respect to :

Now what is ? Again, let's use the chain rule :

hence

Following this idea you can compute . Substituting and by their expressions in terms of and in the differential equation will give you the equation you're looking for.

Hope it helps !