The following is an excerpt from Landau's Course on Theoretical Physics Vol.1 Mechanics:
... we should recall the fact that every first-order partial differential equation has a solution depending on an arbitrary function; such a solution is called the general integral of the equation. In mechanical applications, the general integral of the Hamilton-Jacobi equation is less important than a complete integral, which contains as many independent arbitrary constants as there are independent variables.
Can someone clarify what's a complete integral and what's a general integral of a first order partial differential equation?
Thanks.