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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. >>

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marked as duplicate by user21, Dr. belisarius, Sjoerd C. de Vries, MarcoB, m_goldberg Oct 12 '15 at 21:21

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