ecuacions diferencials y potencia para-integral

d_{x}[y(x)]·d_{xx}^{2}[y(x)] = d_{x}[f(x)]

y(x) = ( f(x) )^{[o(+)o](1/2)}

... ( f(x) )^{[o(+)o](1/2)} [o(x)o] ...

... ( f(x) )^{[o(+)o](-1)(1/2)} [o(x)o] f(x)

d_{x}[y(x)]·d_{xx}^{2}[y(x)]·d_{xxx}^{3}[y(x)] = d_{x}[f(x)]

y(x) = ( f(x) )^{[o(+)o](1/3)}

... ( f(x) )^{[o(+)o](1/3)} [o(x)o] ...

... ( f(x) )^{[o(+)o](-1)(2/3)} [o(x)o] f(x) [o(x)o] ...

... ( f(x) )^{[o(+)o](-1)(5/3)} [o(x)o] ( f(x) )^{[o(+)o]2}

d_{x}[y(x)]·d_{xx}^{2}[y(x)]·d_{xxx}^{3}[y(x)]·d_{xxxx}^{4}[y(x)] = d_{x}[f(x)]

y(x) = ( f(x) )^{[o(+)o](1/4)}

... ( f(x) )^{[o(+)o](1/4)} [o(x)o] ...

... ( f(x) )^{[o(+)o](-1)(3/4)} [o(x)o] f(x) [o(x)o] ...

... ( f(x) )^{[o(+)o](-1)(7/4)} [o(x)o] ( f(x) )^{[o(+)o]2} [o(x)o] ...

... ( f(x) )^{[o(+)o](-1)(11/4)} [o(x)o] ( f(x) )^{[o(+)o]3}

d_{x}[y(x)]·d_{xx}^{2}[y(x)]·d_{xxx}^{3}[y(x)]·d_{xxxx}^{4}[y(x)]·d_{xxxxx}^{5}[y(x)] = d_{x}[f(x)]

y(x) = ( f(x) )^{[o(+)o](1/5)}

... ( f(x) )^{[o(+)o](1/5)} [o(x)o] ...

... ( f(x) )^{[o(+)o](-1)(4/5)} [o(x)o] f(x) [o(x)o] ...

... ( f(x) )^{[o(+)o](-1)(9/5)} [o(x)o] ( f(x) )^{[o(+)o]2} [o(x)o] ...

... ( f(x) )^{[o(+)o](-1)(14/5)} [o(x)o] ( f(x) )^{[o(+)o]3} [o(x)o] ...

... ( f(x) )^{[o(+)o](-1)(19/5)} [o(x)o] ( f(x) )^{[o(+)o]4}

d_{x}[ ( f(x) )^{[o(+)o](m/n)} [o(x)o] ( f(x) )^{[o(+)o]p} ] = ...

... ( f(x) )^{[o(+)o]((m/n)+(-1))} [o(x)o] ( f(x) )^{[o(+)o](p+1)}

d_{x}[y(x)]·...(n)...·d_{x...(n)...x}^{n}[y(x)] = e^{nx}

y(x) = e^{x}

d_{x}[y(x)]·...(n)...·d_{x...(n)...x}^{n}[y(x)] = ( 1/n^{( (1/2)·n(n+1) )}) )·e^{x}

y(x) = e^{(x/n)}