ecuació diferencial potencia integral elíptica

ecuació diferencial elíptica:
d_{xx}^{2}[y(x)] + k·d_{x}[y(x)]^{n} = (-1)^{(-1)/(n+(-1))}·k·( cotan( (n+(-1))k·x ) )^{(n+(-2))/(n+(-1))}


y(x) = ∫ [ ( (-1)·tan( (n+(-1))k ) )^{1/(n+(-1))} ] d[x]


(-1)·k·( (-1)·cotan( (n+(-1))k ) )^{(-n)/(n+(-1))}·( 1+( cotan( (n+(-1))k·x ) )^{2}) +...
... k·( (-1)·tan( (n+(-1))k ) )^{n/(n+(-1))} = (-1)^{(-1)/(n+(-1))}·k·( cotan( (n+(-1))k·x ) )^{(n+(-2))/(n+(-1))}


d_{xx}^{2}[y(x)] + k·d_{x}[y(x)]^{n} = (-1)·k·( tan( (n+(-1))k·x ) )^{(n+(-2))/(n+(-1))}


y(x) = ∫ [ ( cotan( (n+(-1))k ) )^{1/(n+(-1))} ] d[x]


(-1)·k·( tan( (n+(-1))k ) )^{(-n)/(n+(-1))}( 1+( tan( (n+(-1))k·x ) )^{2}) +...
... k·( cotan( (n+(-1))k ) )^{n/(n+(-1))} = (-1)·k·( tan( (n+(-1))k·x ) )^{(n+(-2))/(n+(-1))}


elíptiques sin(x):
f(x) = ( sin( (n+(-1))k·x ) )^{1/(n+(-1))}


( ∫ [ sin( (n+(-1))k·x ) ] d[x]·(n+(-1))·k )^{(-1)/(n+(-1))}·d_{x}[( sin( (n+(-1))k·x ) )^{1/(n+(-1))}]


∫ [ ( (-1)·cos( (n+(-1))k·x ) )^{(-1)/(n+(-1))}·d_{x}[( sin( (n+(-1))k·x ) )^{1/(n+(-1))}] ] d[x] =...
...( (-1)·sin( (n+(-1))k·x ) )^{[o(x)o](-1)/(n+(-1))} [o(x)o] ...
...( (-1)·cos( (n+(-1))k·x ) )^{[o(x)o]((-n)+2)/(n+(-1))} [o(x)o] ...
... sin( (n+(-1))k·x ) [o(x)o] kx = ..


... (-1)·k·( tan[o(x)o]( (n+(-1))k·x ) )^{[o(x)o](n+(-2))/(n+(-1))} = ...
... (-1)^{(-1)(n+(-1))/(n+(-1))}·k·( tan[o(x)o]( (n+(-1))k·x ) )^{[o(x)o](n+(-2))/(n+(-1))} = ...
... (-1)^{((-n)+1)/(n+(-1))}·k· ∫ [ ( (-1)·cotan( (n+(-1))k·x ) )^{(n+(-2))/(n+(-1))} ] d[x] = ...
... (-1)^{(-1)/(n+(-1))}·k· ∫ [ ( cotan( (n+(-1))k·x ) )^{(n+(-2))/(n+(-1))} ] d[x]


elíptiques cos(x):
f(x) = ( cos( (n+(-1))k·x ) )^{1/(n+(-1))}


( ∫ [ cos( (n+(-1))k·x ) ] d[x]·(n+(-1))·k )^{(-1)/(n+(-1))}·d_{x}[( cos( (n+(-1))k·x ) )^{1/(n+(-1))}]


∫ [ ( sin( (n+(-1))k·x ) )^{(-1)/(n+(-1))}·d_{x}[( cos( (n+(-1))k·x ) )^{1/(n+(-1))}] ] d[x] =...
...( (-1)·cos( (n+(-1))k·x ) )^{[o(x)o](-1)/(n+(-1))} [o(x)o] ...
...( sin( (n+(-1))k·x ) )^{[o(x)o]((-n)+2)/(n+(-1))} [o(x)o] ...
... cos( (n+(-1))k·x ) [o(x)o] kx = ..


... (-1)^{(-1)/(n+(-1))}·k·( cotan[o(x)o]( (n+(-1))k·x ) )^{[o(x)o](n+(-2))/(n+(-1))} =...
... (-1)^{(-1)/(n+(-1))}·k· ∫ [ ( (-1)^{(-1)}·tan( (n+(-1))k·x ) )^{(n+(-2))/(n+(-1))} ] d[x] =...
... (-1)·k· ∫ [ ( tan( (n+(-1))k·x ) )^{(n+(-2))/(n+(-1))} ] d[x]