Is there any solution to eliminate function p[x,y] from these two equations which are equal to zero (diff1==0 and diff2==0), where c and d are constants. I need one equation where should figure just w[x,y] and u[x,y]. I have already tried this:

Eliminating functions from system of PDE in Mathematica

but without success. Probably it is necessary more times to do the differentiation but I am not sure how to handle it.

diff1 = c1*Derivative[0, 2][w][x, y] - 
   c2*Derivative[1, 0][p][x, y] + 
   c3*Derivative[1, 2][p][x, y] - 
   c4*Derivative[1, 0][w][x, y]*
     Derivative[2, 0][u][x, y] - 
   c5*Derivative[1, 0][u][x, y]*
     Derivative[2, 0][w][x, y] + 
   c6*Derivative[2, 0][w][x, y] - 
   c7*Derivative[1, 0][w][x, y]^2*
     Derivative[2, 0][w][x, y] - 
   c8*Derivative[2, 2][w][x, y] + 
   c9*Derivative[3, 0][p][x, y] + 
   c10*Derivative[4, 0][w][x, y]; 

diff2 = d1*p[x, y] + d2*Derivative[0, 2][p][
       x, y] + d3*Derivative[1, 0][w][x, 
       y] + d4*Derivative[1, 2][w][x, y] - 
   d5*Derivative[2, 0][p][x, y] + 
   d6*Derivative[3, 0][w][x, y]; 
  • $\begingroup$ Typically, three PDEs are needed to solve for three dependent variables. Eliminating one dependent variable typically requires eliminating one PDE, also leaving one PDE too few to solve for the remaining two dependent variables. $\endgroup$ – bbgodfrey Jan 18 '16 at 8:37
  • $\begingroup$ of course. I need one PDE but without p(x,y) $\endgroup$ – Pipe Jan 18 '16 at 13:18

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