ecuacions diferencials de potencia integral

x^{n}·d_{x...x}^{n}[f(x)] = f(x)
f(x) = e^{[o(x)o]^{n+(-1)}( (-1)^{n+(-1)}/(n+(-1))! )·ln(x)}




d_{x}[ e^{[o(x)o]^{n}f(x)} ] = ∫ ...(n)... ∫ [ e^{[o(x)o]^{n}f(x)} ] d[x]...(n)...d[x] [o(x)o]^{n} d_{x}[f(x)]



x·d_{x}[f(x)] = f(x)


f(x) = e^{[o(x)o]^{0}ln(x)}
d_{x}[f(x)] = e^{[o(x)o]^{0}ln(x)}·(1/x)
d_{x}[f(x)] = e^{ln(x)}·(1/x) = x·(1/x) = 1


x^{2}·d_{xx}^{2}[f(x)] = f(x)


f(x) = e^{[o(x)o]^{1}(-1)·ln(x)}
d_{x}[f(x)] = ∫ [e^{[o(x)o]^{1}(-1)·ln(x)} ] d[x] [o(x)o] (-1)·(1/x)
d_{xx}^{2}[f(x)] = e^{[o(x)o]^{1}(-1)·ln(x)}·(1/x^{2})


x^{3}·d_{xxx}^{3}[f(x)] = f(x)


f(x) = e^{[o(x)o]^{2}(1/2!)·ln(x)}
d_{x}[f(x)] = ∫ ∫ [ e^{[o(x)o]^{2}(1/2!)·ln(x)} ] d[x]d[x] [o(x)o]^{2} (1/2!)·(1/x)
d_{xx}^{2}[f(x)] = ∫ [ e^{[o(x)o]^{2}(1/2!)·ln(x)} ] d[x] [o(x)o] (1/2!)(-1)·(1/x^{2})
d_{xxx}^{3}[f(x)] = e^{[o(x)o]^{2}(1/2!)·ln(x)}·(1/x^{3})