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];