bi-elípticas y bi-hiperbólicas

d_{t}[z(t)] = a·h^{m+1}+b·( n^{n+1}+(-1)·y^{n+1} )^{( (m+1)/(n+1) )}

z(t) = ( (-1)·( cos[h^{m+1},y^{n+1}](at) )^{[o(t)o](m+1)}+( sin[h^{m+1},y^{n+1}](bt) )^{[o(t)o](m+1)} )

h(t) = sin[h^{m+1},y^{n+1}](at)

y(t) = sin[h^{m+1},y^{n+1}](bt)

d_{tt}^{2}[y(t)] = (-1)·qg+2F·( y/( x^{2}+y^{2} )^{(1/2)} )

d_{t}[y(t)]^{2} = (-1)·qgy+2F·( x^{2}+y^{2} )^{(1/2)}

d_{t}[z(t)]^{2} = (-1)·qgh+2F·( x^{2}+y^{2} )^{(1/2)}

y(t) = norm[(z(t),h(t))-->y(t)][ ( (-1)·( cosh[h,y^{2}]( qg·t ) )+( sinh[h,y^{2}]( 2F·x^{3}·t ) ) )^{[o(t)o](1/2)} ]

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

d_{tt}^{2}[x(t)] = (-1)·kx+2F·( x/( y^{2}+x^{2} )^{(1/2)} )

d_{t}[x(t)]^{2} = (-1)·(1/2)·kx^{2}+2F·( y^{2}+x^{2} )^{(1/2)}

d_{t}[z(t)]^{2} = (-1)·(1/2)·kh^{2}+2F·( y^{2}+x^{2} )^{(1/2)}

x(t) = norm[(z(t),h(t))-->x(t)][ ...

... ( ( cosh[h^{2},x^{2}]( (1/2)·k·t ) )+( sinh[h^{2},x^{2}]( 2F·y^{3}·t ) )^{[o(t)o](1/2)} )^{[o(t)o](1/2)} ...

... ]

funciones elípticas:

( cos[n](t) )^{n+1}+( sin[n](t) )^{n+1} = n^{(n+1)}

( cos[p](t) )^{p+1}+( sin[q](t) )^{q+1} = ( (p+q)/2 )^{((p+1)/2)+((q+1)/2)}

( sin[p](t) )^{p+1}+( cos[q](t) )^{q+1} = ( (p+q)/2 )^{((p+1)/2)+((q+1)/2)}

d_{t}[sin[p](t)] = cos[p](t)

d_{t}[sin[q](t)] = cos[q](t)

d_{t}[cos[p](t)] = (-1)·sin[p](t)

d_{t}[cos[q](t)] = (-1)·sin[q](t)