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August 21st, 2013, 05:59 AM   #1
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Partial Differential Differential Equations

Suppose I have a partial differential equation Pp+Qq=R. NOw I wish to find a complete integral of this equation. If I use condition 1(given in some form of relations) and find out a family of surfaces given by F(x,y,z,a,b)=0. If using a different condition( say condition 2) I arrive at another family of surfaces, say G(x,y,z,c,d)=0. Is it possible that these two families of surfaces intersect along a curve.
If yes, then suppose you are given the constraints of the common curve. Which surface would you obtain by using these constraints? F or G or a combination of both?
An illustration would be extremely helpful.
Thanks!
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