martes, 13 de octubre de 2020

sistemes de ecuacions diferencials

d_{t}[x(t)] = a·y(t)

d_{t}[x(t)] = b·z(t)

x(t) = (ab)·(1/(n+1))·t^{n+1}

y(t) = b·t^{n}

z(t) = a·t^{n}


d_{t}[x(t)] = a·e^{y(t)}

d_{t}[x(t)] = b·e^{z(t)}

x(t) = (ab)·(1/(n+1))·t^{n+1}

y(t) = ln(bt^{n})

z(t) = ln(at^{n})


d_{t}[x(t)] = a·ln(y(t))

d_{t}[x(t)] = b·ln(z(t))

x(t) = (ab)·(1/(n+1))·t^{n+1}

y(t) = e^{bt^{n}}

z(t) = e^{at^{n}}


d_{t}[x(t)] = a·( y(t) )^{p}

d_{t}[x(t)] = b·( z(t) )^{q}

x(t) = (ab)·(1/(n+1))·t^{n+1}

y(t) = b^{(1/p)}·t^{(n/p)}

z(t) = a^{(1/q)}·t^{(n/q)}


d_{t}[x(t)] = a·( y(t) )^{p}·f(y(t))

d_{t}[x(t)] = b·( z(t) )^{q}·f(z(t))

x(t) = (ab)·(1/(n+1))·t^{n+1}

y(t) = f-pow[p]( bt^{n} )

z(t) = f-pow[q]( at^{n} )


d_{t}[x(t)] = a·e^{u·y(t)}f(y(t))

d_{t}[x(t)] = b·e^{v·z(t)}·f(z(t))

x(t) = (ab)·(1/(n+1))·t^{n+1}

y(t) = f-e[u]( bt^{n} )

z(t) = f-e[v]( at^{n} )


d_{t}[x(t)] = a·( y(t) )^{p}·e^{u·y(t)}f(y(t))

d_{t}[x(t)] = b·( z(t) )^{q}·e^{v·z(t)}·f(z(t))

x(t) = (ab)·(1/(n+1))·t^{n+1}

y(t) = f-e[u]-pow[p]( bt^{n} )

z(t) = f-e[v]-pow[q]( at^{n} )


d_{t}[x(t)] = a·y(t)+(b/n)·t·d_{t}[z(t)]

d_{t}[x(t)] = b·z(t)+(a/n)·t·d_{t}[y(t)]

x(t) = (ab)·(1/(n+1))·t^{n+1}

y(t) = (b/2)·t^{n}

z(t) = (a/2)·t^{n}


d_{t}[x(t)] = a·e^{y(t)}+(b/n)·t·e^{z(t)}·d_{t}[z(t)]

d_{t}[x(t)] = b·e^{z(t)}+(a/n)·t·e^{y(t)}·d_{t}[y(t)]

x(t) = (ab)·(1/(n+1))·t^{n+1}

y(t) = ln((b/2)·t^{n})

z(t) = ln((a/2)·t^{n})

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