ecuació diferencial de tercer ordre

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


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


(1/6)·d_{x}[f(x)]^{([o(x)o] 2) [o(+)o] 1} = ∫ ∫ [g(x)] d[x]d[x]


f(x) = ∫ ( 6·∫ ∫ [g(x)] d[x]d[x] )^{(1/(([o(x)o] 2) [o(+)o] 1))} d[x]


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


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


(1/6)·d_{x}[f(x)]^{([o(x)o] 2) [o(+)o] 1} [o(x)o]^{2} d_{xx}^{2}[f(x)] = ∫ ∫ [g(x)] d[x]d[x]


(1/24)·d_{x}[f(x)]^{(([o(x)o] 2) [o(+)o] 1) [o(+)o]^{2} 1} = ∫ ∫ ∫ [g(x)] d[x]d[x]d[x]


f(x) = ∫ ( 24·∫ ∫ ∫ [g(x)] d[x]d[x]d[x] )^{(1/((([o(x)o] 2) [o(+)o] 1) [o(+)o]^{2} 1))} d[x]


∫ ( f(x) )^{n} [o(x)o] d_{x}[f(x)] d[x] = ( 1/(n+1) )·( f(x) )^{([o(x)o] n) [o(+)o] 1}
∫ ( f(x) )^{n} [o(x)o]^{p} d_{x}[f(x)] d[x] = ( 1/(n+1) )·( f(x) )^{([o(x)o] n) [o(+)o]^{p} 1}