I'm trying to solve the following PDE but I'm getting this error. The PDE represents the bending of a thin plate.
NDSolve[{
D[w[x, y], {x, 4}] + D[w[x, y], {y, 4}] + D[w[x, y], x, y, x,y] == 10,
w[0, y] == 0,
w[x, 0] == 0,
w[5, y] == 0,
w[x, 3] == 0,
D[w[0, y], {y, 2}] == 0,
D[w[5, y], {y, 2}] == 0,
D[w[x, 0], {x, 2}] == 0,
D[w[x, 3], {x, 2}] == 0},
w, {x, 0, 5}, {y, 0, 3}]
The error is:
NDSolve::femcmsd: The spatial derivative order of the PDE may not exceed two. >>
