ecuacions en derivades parcials

u(x,y) = f(x)+g(y)

d_{x}[f(x)+g(y)] = d_{y}[f(x)+g(y)]

d_{x}[f(x)] = a & a = d_{y}[g(y)]

d_{x}[f(x)] = (-a) & (-a) = d_{y}[g(y)]

d_{x}[u(x,y)] = d_{y}[u(x,y)]

u(x,y) = ax+ay || u(x,y) = (-a)·x+(-a)·y

d_{x}[u(x,y)] = (-1)·d_{y}[u(x,y)]

u(x,y) = ax+(-a)·y || u(x,y) = (-a)·x+ay

d_{x}[u(x,y)] = i·d_{y}[u(x,y)]

u(x,y) = ai·x+ay || u(x,y) = (-a)i·x+(-a)y

u(x,y) = (-a)x+ai·y || u(x,y) = ax+(-a)i·y

d_{x}[u(x,y)] = (-i)·d_{y}[u(x,y)]

u(x,y) = (-a)i·x+ay || u(x,y) = ai·x+(-a)y

u(x,y) = (-a)·x+(-a)i·y || u(x,y) = ax+ai·y

e^{u(x,y)}( d_{x}[u(x,y)]+d_{y}[u(x,y)] ) = k^{2}·(x+y)

u(x,y) = ln( kx )+ln( ky ) || u(x,y) = ln( (-k)x )+ln( (-k)y )

e^{u(x,y)}( d_{x}[u(x,y)]+d_{y}[u(x,y)] ) = (-1)·k^{2}·(x+y)

u(x,y) = ln( kx )+ln( (-k)y ) || u(x,y) = ln( (-k)x )+ln( ky )