ecuacions diferencials pow-put y e-put y log-put

ln(( h(y) )^{m}+a_{1}) [o(t)o] ...(n)... [o(t)o] ln(( h(y) )^{m}+a_{n}) = vt [o(t)o] ( ( h(y) )^{m} )^{[o(y)o]n}

ln-[o(t)o]-h-put[m]-[a_{1},...,a_{n}](y) = vt

y = h-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(vt)

d_{y}[ pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(y) ] = ...

... (( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(y) )^{m}+a_{1})·...

... (n) ...

... (( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(y) )^{m}+a_{n})

d_{y}[ e-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(y) ] = ...

... (( e^{e-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(y)} )^{m}+a_{1})·...

... (n) ...

... (( e^{e-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(y)} )^{m}+a_{n})

d_{y}[ log-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(y) ] = ...

... (( ln(log-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(y)) )^{m}+a_{1})·...

... (n) ...

... (( ln(log-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(y)) )^{m}+a_{n})

d_{t}[z(y)] = v·y^{n+(-1)}(y^{m}+a_{1})·...(n)...·(y^{m}+a_{n})

z(t) = (1/n)·( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(vt) )^{n}

d_{t}[z(y)] = v·(1/y)·(y^{m}+a_{1})·...(n)...·(y^{m}+a_{n})

z(t) = ln( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(vt) )

d_{t}[z(y)] = v·e^{ny}·(y^{m}+a_{1})·...(n)...·(y^{m}+a_{n})

z(t) = (1/n)·e^{n·( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(vt) )}

d_{t}[z(y)] = v·d_{y}[g(y)]·(y^{m}+a_{1})·...(n)...·(y^{m}+a_{n})

z(t) = g( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(vt) )

d_{t}[z(y)] = ...

... v·( d_{y}[f_{1}(y)]+...(p)...+d_{y}[f_{p}(y)] )·(y^{m}+a_{1})·...(n)...·(y^{m}+a_{n})

z(t) = ...

... f_{1}( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(vt) )+...

... (p) ...

... f_{p}( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(vt) )

d_{t}[z(y)] = ...

... v·( (y^{p+1}+(-1))/(y+(-1)) )·(y^{m}+a_{1})·...(n)...·(y^{m}+a_{n})

z(t) = ...

... ( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(vt) )+...

... (p) ...

... (1/(p+1))·( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(vt) )^{p+1}

d_{t}[z(y)] = ...

... v·( (y^{m}+a_{1})·...(n)...·(y^{m}+a_{n}) )^{p}

z(t) = ( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(v^{(1/p)}·t) )^{[o(t)o]p}

d_{t}[z(y)] = ...

... v·( y·(y^{m}+a_{1})·...(n)...·(y^{m}+a_{n}) )^{p}

z(t) = ( (1/2)·( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(v^{(1/p)}·t) )^{2} )^{[o(t)o]p}

d_{t}[z(y)] = ...

... v·( d_{y}[g(y)]·(y^{m}+a_{1})·...(n)...·(y^{m}+a_{n}) )^{p}

z(t) = ( g( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(v^{(1/p)}·t) ) )^{[o(t)o]p}

d_{t}[z(y)] = ...

... v·y^{q}·( (y^{m}+a_{1})·...(n)...·(y^{m}+a_{n}) )^{p}

z(t) = ( (p/(q+p))·( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(v^{(1/p)}·t) )^{((q+p)/p)} )^{[o(t)o]p}

d_{t}[z(y)] = ...

... v·d_{y}[g(y)]^{q}·( (y^{m}+a_{1})·...(n)...·(y^{m}+a_{n}) )^{p}

z(t) = ...

... ( (p/(q+p))·( d_{pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(v^{(1/p)}·t)}[ ...

... g( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(v^{(1/p)}·t) ) ...

... ] )^{((q+p)/p)} )^{[o(t)o]p} ...

... [o(t)o] d_{pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(v^{(1/p)}·t)}[ ...

... g( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(v^{(1/p)}·t) ) ...

... ]^{[o( pow-put[m]-[a_{1},...,a_{n}]-[o(t)o]-e(v^{(1/p)}·t) )o](-p)}

int[ d_{t}[z(y)]^{p} ] d[t] = int[ d_{y}[z(y)]^{p}·d_{t}[y]^{p} ] d[t]