sistemes en derivades parcials

d_{x}[u(x,y,z)]+(-1)·(1/x)·u(x,y,z) = 0

d_{y}[u(x,y,z)]+(-1)·(1/y)·u(x,y,z) = 0

d_{z}[u(x,y,z)]+(-1)·(1/z)·u(x,y,z) = 0

u(x,y,z) = xyz

d_{x}[u(x,y,z)]+(-1)·(n/x)·u(x,y,z) = 0

d_{y}[u(x,y,z)]+(-1)·(n/y)·u(x,y,z) = 0

d_{z}[u(x,y,z)]+(-1)·(n/z)·u(x,y,z) = 0

u(x,y,z) = n·xyz

d_{x}[u(x,y)]+y·u(x,y) = f(x)

d_{y}[u(x,y)]+x·u(x,y) = f(y)

u(x,y) = e^{(-x)·y}·int[ f(x)·e^{xy} ] d[x]+e^{(-y)·x}·int[ f(y)·e^{yx} ] d[y]

e^{(-y)·x}·d_{x}[ int[ f(y)·e^{yx} ] d[y] ] = f(y)·d_{x}[y] = 0

d_{x}[u(x,y)]+(2/x)·u(x,y) = x

d_{y}[u(x,y)]+(2/y)·u(x,y) = y

u(x,y) = (x/y)+(-1)·(1/y^{2})+(y/x)+(-1)·(1/x^{2})

y = (2/x) & x = (2/y)

(2/x)·u(x,y) = (2/x)·(x^{2}/2)+(-1)·(2/x)·(x^{2}/4)+(2/x)·(2/x^{2})+(-1)·(2/x)·(1/x^{2})

(2/y)·u(x,y) = (2/y)·(2/y^{2})+(-1)·(2/y)·(1/y^{2})+(2/y)·(y^{2}/2)+(-1)·(2/y)·(y^{2}/4)