ecuacions diferencials

d_{x}[ ka-x[n](x) ] = ( x/(x+ka-x[n](x))^{n} )

d_{y}[ ak-x[n](y) ] = ( (ak-x[n](y)+y)^{n}/(ak-x[n](y)) )

d_{x}[ ka-y[n](x) ] = ( (ka-y[n](x)+x)^{n}/x )

d_{y}[ ak-y[n](y) ] = ( (ak-y[n](y))/(y+ak-y[n](y))^{n} )

d_{x}[y(x)] = ( x/(x+y) )

y(x) = ka-x[1](x)

d_{x}[y(x)] = ( (x+y)/x )

y(x) = ka-y[1](x)

d_{x}[y(x)] = ( x^{2}+xy )

y(x) = ka-x[(-1)](x)

d_{x}[y(x)] = ( 1/(x^{2}+xy) )

y(x) = ka-y[(-1)](x)

d_{x}[y(x)] = ( (y+x)/y )

y(x) = ak-x[1](x)

d_{x}[y(x)] = ( y/(y+x) )

y(x) = ak-y[1](x)

d_{x}[y(x)] = ( 1/(y^{2}+xy) )

y(x) = ak-x[(-1)](x)

d_{x}[y(x)] = ( y^{2}+xy )

y(x) = ak-y[(-1)](x)

d_{x}[ kak[n][a,b](x) ] = ( (ax+b·kak[n](x))/(x+kak[n](x))^{n} )

d_{y}[ aka[n][a,b](y) ] = ( (aka[n](y)+y)^{n}/(a·aka[n](y)+by) )

d_{x}[ kak[n][a,a](x) ] = a·d_{x}[ kak[n][1,1](x) ]

d_{y}[ aka[n][a,a](y) ] = (1/a)·d_{y}[ aka[n][1,1](y) ]

kak[n][1,0](x) = ka-x[n](x)

aka[n][1,0](y) = ak-x[n](y)

kak[n][0,1](y) = ak-y[n](y)

aka[n][0,1](x) = ka-y[n](x)

d_{x}[y(x)] = ( (ax+by)/(x+y)^{n} )

y(x) = kak[n][a,b](x)

d_{x}[y(x)] = ( (x+y)^{n}/(ax+by) )

y(x) = aka[n][b,a](x)

d_{x}[y(x)] = ( (ax+by)·(x+y)^{n} )

y(x) = kak[(-n)][a,b](x)

d_{x}[y(x)] = ( 1/((x+y)^{n}·(ax+by)) )

y(x) = aka[(-n)][b,a](x)