ecuacions diferencials sinus-polinomi

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

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

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

... f^{o(-1)}( f(x^{m}) ) = x^{m}

d_{x}[ sin[(-n)]-[o(t)o]-ln( f(x^{m}) ) ] = ...

... (1/f(x^{m}))·d_{x}[f(x^{m})]·(-n)·( sin(x) )^{(-1)·(n+1)})·cos(x)

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

... e-[o(t)o]-sin[(-n)](y)·...

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

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

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

d_{t}[y] = ...

... ( ((cd)·cos(d))/(( sin(d) )^{n+1}·d^{m}) )·( 1/(b^{m}+(-1)·a^{m}) )·...

... ( 1/cos(y) )·( sin(y) )^{n+1}·(y^{m}+a^{m})·(y^{m}+b^{m})

y(t) = ...

... ( ...

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

... (-1)·b^{m}...

... )^{(1/m)}

d_{t}[z] = ...

... ( ((cd)·cos(d))/(( sin(d) )^{n+1}·d^{m}) )·...

... ( 1/cos(z) )·( sin(z) )^{n+1}·(z^{m}+a^{m})

z(t) = ...

... ( ( e-[o(t)o]-sin[(-n)]((-n)·( ((cd)·cos(d))/(( sin(d) )^{n+1}·d^{m}) )·t) )+(-1)·a^{m} )^{(1/m)}