sistemes de ecuacions diferencials

sistema:

d_{t}[x(t)] = y(t)+z(t)

d_{t}[y(t)] = z(t)+x(t)

d_{t}[z(t)] = x(t)+y(t)

ecuación diferencial asociada al sistema:

d_{tt}^{2}[x(t)] = d_{t}[x(t)]+2·x(t)

d_{tt}^{2}[y(t)] = d_{t}[y(t)]+2·y(t)

d_{tt}^{2}[z(t)] = d_{t}[z(t)]+2·z(t)

k = (1/2)·( 1+3 ) = 2

x(t) = e^{2t}

y(t) = e^{2t}

z(t) = e^{2t}

sistema:

d_{t}[x(t)] = e^{y(t)}+e^{z(t)}

d_{t}[y(t)] = e^{z(t)}+e^{x(t)}

d_{t}[z(t)] = e^{x(t)}+e^{y(t)}

 

e^{2·x(t)} = e^{y(t)}e^{z(t)}

e^{2·y(t)} = e^{z(t)}e^{x(t)}

e^{2·z(t)} = e^{x(t)}e^{y(t)}

ecuación diferencial asociada a los sistemas:

d_{tt}^{2}[x(t)] = 2e^{2·x(t)}+e^{x(t)}·d_{t}[x(t)]

d_{tt}^{2}[y(t)] = 2e^{2·y(t)}+e^{y(t)}·d_{t}[y(t)]

d_{tt}^{2}[z(t)] = 2e^{2·z(t)}+e^{z(t)}·d_{t}[z(t)]

x(t) = ln(1/((-2)·t))

y(t) = ln(1/((-2)·t))

z(t) = ln(1/((-2)·t))

sistema:

d_{t}[x(t)] = ln(y(t))·y(t)+ln(z(t))·z(t)

d_{t}[y(t)] = ln(z(t))·z(t)+ln(x(t))·x(t)

d_{t}[z(t)] = ln(x(t))·x(t)+ln(y(t))·y(t)

2·( ln(x(t)) )^{2}·x(t) = ln(y(t))·ln(z(t))·( y(t)+z(t) )

2·( ln(y(t)) )^{2}·y(t) = ln(z(t))·ln(x(t))·( z(t)+x(t) )

2·( ln(z(t)) )^{2}·z(t) = ln(x(t))·ln(y(t))·( x(t)+y(t) )

2·( ln(x(t)) )^{2}·x(t) = ln(x(t))·x(t)·( ln(y(t))+ln(z(t)) )

2·( ln(y(t)) )^{2}·y(t) = ln(y(t))·y(t)·( ln(z(t))+ln(x(t)) )

2·( ln(z(t)) )^{2}·z(t) = ln(z(t))·z(t)·( ln(x(t))+ln(y(t)) )

ecuación diferencial asociada a los sistemas:

d_{tt}^{2}[x(t)] = d_{t}[x(t)]+2·ln(x(t))·x(t)+4·( ln(x(t)) )^{2}·x(t)

d_{tt}^{2}[y(t)] = d_{t}[y(t)]+2·ln(y(t))·y(t)+4·( ln(y(t)) )^{2}·y(t)

d_{tt}^{2}[z(t)] = d_{t}[z(t)]+2·ln(z(t))·z(t)+4·( ln(z(t)) )^{2}·z(t)

x(t) = e^{e^{2t}}

y(t) = e^{e^{2t}}

z(t) = e^{e^{2t}}