if we have an implicit function eqn1
then we can find the standard derivative eqn 2 and
the partial derivative eqn3
However, I am trying to grasp the idea of having a standard/total derivation and partial derivation of functions as above yet we dont have standard or partial integration (ie the reverse). How is that?
If we integrate back eqn2 wrt to x we get eqn1 with a constant. This constant can be determined if BC's or IC's are known (ie 6) etc...but
if we integrate eqn3 wrt x we can get eqn1 with a constant also but we lose the term. How does one get this term back?
I dont think I understand this fully. Can anyone shed some light?