ecuació diferencial potencia integral hiperbólica

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


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


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


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


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


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


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


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


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


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


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


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


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


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