ecuacions diferencials logaritme-polinomi

int[ d_{x}[f(x^{m})] ] d[x] = ...

... f(x^{m}) = f(x^{m})

int[ d_{( f^{o(-1)}( e-[o(t)o]-ln[(-n)](y) ) )^{(1/m)}}[f^{o(-1)}( e-[o(t)o]-ln[(-n)](y) )] ] d[x] = ...

... f^{o(-1)}( f(x^{m}) ) = x^{m}

d_{x}[ ln[(-n)]-[o(t)o]-ln( f(x^{m}) ) ] = (1/f(x^{m}))·d_{x}[f(x^{m})]·(-n)·( ln(x) )^{(-1)·(n+1)})·(1/x)

d_{y}[ e-[o(t)o]-ln[(-n)](y) ] = ...

... e-[o(t)o]-ln[(-n)](y)·...

... d_{( f^{o(-1)}( e-[o(t)o]-ln[(-n)](y) ) )^{(1/m)}}[f^{o(-1)}( e-[o(t)o]-ln[(-n)](y) )]·...

... (1/(-n))·( f^{o(-1)}( e-[o(t)o]-ln[(-n)](y) ) )^{(1/m)}·...

... ( ln( ( f^{o(-1)}( e-[o(t)o]-ln[(-n)](y) ) )^{(1/m)} ) )^{n+1}

d_{t}[y] = ...

... ( c/(( ln(d) )^{n+1}·d^{m}) )·(1/(b^{m}+(-1)·a^{m}))·...

... y·( ln(y) )^{n+1}·(y^{m}+a^{m})·(y^{m}+b^{m})

y(t) = ...

... ( ( (a^{m}+(-1)·b^{m})/(e-[o(t)o]-ln[(-n)]((-n)·( c/(( ln(d) )^{n+1}·d^{m}) )·t)+(-1)) )+(-1)·b^{m} )^{(1/m)}