I am looking to solve the following equations numerically:
For arbitrary functions f and g and constants a and b. I am struggling to find a way to transform this into a system of first order differential equations that I can pass into a solver. It looks like I will need to define these implicitly, but I'm not sure how to do that.
My best attempt so far is the following:
However, this seems fairly inelegant and assumes that you are always able to divide by f and g. I'm trying to keep this as general as possible, so don't want to make that assumption. Is there a better way to turn this into a system of first order differential equations implicitly?