ecuació diferencial de lagranià II

( x [+] y )^{n} = x^{n} + y^{n}
( x [+] y ) = x+y


( x [+] y ) = u^{p}+v^{q}
( x [+] y )^{n} = u^{pn}+v^{qn}




d_{x}[ f(x) [+] g(x) ] = d_{x}[f(x)] [+] d_{x}[g(x)]
d_{x}[ f(x) [·] g(x) ] = d_{x}[f(x)][·]g(x) [+] f(x)[·]d_{x}[g(x)]


d_{x}[ mix[p/n]( f(x),g(x) ) ] = d_{x}[f(x)]·mix[p/n]( f(x),g(x) )^{(p/n)} [+] g(x)


mix[1]( f(x),g(x) ) = e^{f(x)}[·]int[ g(x)[·]e^{(-1)f(x)} ]d[x]


c·d_{t}[y(t)]^{n}+a(t)( y(t) )^{p}=g(t)


y(t)=mix[p/n]( (1/c^{(1/n)})·int[(-a(t))^{(1/n)}]d[x] , (1/c^{(1/n)})·(g(t))^{(1/n)} )