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]

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)}

ecuacions diferencials exponencial-polinomi

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

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

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

... f^{o(-1)}( f(x^{m}) ) = x^{m}

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

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

... e-[o(t)o]-e[(-n)](y)·...

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

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

d_{t}[y] = ( (cd)/(e^{nd}d^{m}) )·( 1/(b^{m}+(-1)a^{m}) )·e^{ny}·(y^{m}+a^{m})·(y^{m}+b^{m})

y(t) = ...

... ( ...

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

... (-1)·b^{m}...

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

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)}

ecuacions diferencials

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

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

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

... f^{o(-1)}( f(x^{m}) ) = x^{m}

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

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

... e-[o(t)o]-pow[(-n)](y)·...

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

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

d_{t}[y] = ...

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

y(t) = ...

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

cinematica: tren de (-b) a b con parada en (-c) y c y zero

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

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

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

... f^{o(-1)}( f(x^{n}) ) = x^{n}

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

d_{y}[ e-[o(t)o]-ln[1](y) ] = ...

... e-[o(t)o]-ln[1](y)·...

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

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

d_{t}[x] = (1/(b^{2}+(-1)·c^{2}))·(a/d^{2})·x(x^{2}+(-1)·c^{2})·(x^{2}+(-1)·b^{2})

x(t) = ( ( (b^{2}+(-1)·c^{2})/(1+(-1)·e-[o(t)o]-ln[1]((a/d^{2})·t)) )+c^{2} )^{(1/2)}

cinematica: tren de (-b) a b con parada en (-c) y c

d_{t}[x] = ( 1/(b^{2}+(-1)·c^{2}) )·(a/(2x))·(x^{2}+(-1)·c^{2})·(x^{2}+(-1)·b^{2})

x^{2} = y+(1/2)·c^{2}+(1/2)·b^{2}

ln( 1+(-1)( (b^{2}+(-1)·c^{2})/(x^{2}+(-1)·c^{2}) ) ) = at

x(t) = ( ( (b^{2}+(-1)·c^{2})/(1+(-1)·e^{at}) )+c^{2} )^{(1/2)}

a·(1/(b^{2}+(-1)·c^{2}))(x^{2}+(-1)·c^{2})(x^{2}+(-1)·b^{2}) = ...

... a·( ( (b^{2}+(-1)·c^{2})·e^{at} )/( 1+(-1)·e^{at} )^{2} )

d_{t}[x] = (1/2)( ( (b^{2}+(-1)·c^{2})/(1+(-1)·e^{at}) )+c^{2} )^{(-1)(1/2)}

... ( ( ( (b^{2}+(-1)·c^{2})·e^{at}a )/(1+(-1)·e^{at})^{2} ) )

x = 0 ==>

( (b^{2}+(-1)·c^{2})/(1+(-1)·e^{at}) ) = (-1)·c^{2}

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

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

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

... f^{o(-1)}( f(x^{n}) ) = x^{n}

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

d_{y}[ e-[o(t)o]-pow[1](y) ] = ...

... e-[o(t)o]-pow[1](y)·...

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

d_{t}[x] = ( 1/(b^{2}+(-1)·c^{2}) )·(a/d)·(x^{2}+(-1)·c^{2})·(x^{2}+(-1)·b^{2})

x(t) = ( ( (b^{2}+(-1)·c^{2})/(1+(-1)·e-[o(t)o]-pow[1]((a/d)·t)) )+c^{2} )^{(1/2)} 

cinematica: tren de (-b) a b con parada en zero

d_{t}[x] = a·( 1/(2b^{2}) )·x( x^{2}+(-1)·b^{2})

( ( 1/(x+(-b)) )+( 1/(x+b) )+(-2)·( 1/x ) )·d_{t}[x] = a

( ( 2x/(x+(-b))(x+b) )+(-2)·( 1/x ) )·d_{t}[x] = a

ln(x+(-b))+ln(x+b)+(-1)·ln(x^{2}) = at

1+(-1)·(b^{2}/x^{2}) = e^{at}

(b^{2}/x^{2}) = 1+(-1)·e^{at}

x(t) = b·( (1+(-1)·e^{at}) )^{(-1)·(1/2)}

d_{t}[x] = (ba)·(1/2)·( (1+(-1)·e^{at}) )^{(-1)·(3/2)}·e^{at}

català-castellàn [ ve-wel ] y [ vo-u ] y [ z-xum ]

llave

llawel

clave

clawel

breve

brewel

leve

lewel

nieve

newel

nueve

nowel

clavo

clau

huevo

hou

nuevo

nueva

nou

nova

bravo

brava

brau

brava

inyectivo

inyectiva

inyectiu

inyectiva

biyectivo

biyectiva

biyectiu

biyectiva

exhaustivo

exhaustiva

exhaustiu

exhaustiva

paz

paxum

vez

vexum

luz

luxum

cruz

cruxum

voz

voxum

pez

pexum

diez

dexum

juez

joxum

verbos traer y extraer --- treure y extreure

traigo

traes

trae

traemos

traéis

traen

traído

traída

trec

treus

treu

treyem

treyeu

treuen

tregut

treguda

traer: objeto de allí a aquí.

treure: objecte de aquí a allà.

extraer: objeto de aquí a allí.

extreure: objecte de allà a aquí.

distraer: de allí a aquí.

distreure: de aquí a allà.

disextraer: de aquí a allí.

disextreure: de allà a aquí.

vengo a distraer a aquí.

vinc a disextreure a aquí.

voy a disextraer a allí.

vaitx a distreure a allà.

extrec pizza a casa de la pizzería.

traigo pizza a casa de la pizzería.

trec la basura.

extraigo la basura.

verbos caer --- caure

caigo

caes

cae

caemos

caéis

caen

caído

caída

caic

caus

cau

cayem

cayeu

cauen

caigut

caiguda

calculo integral

int[ ( g(f(x)) )^{n} ] d[x] = ...

... (1/(n+1))·( g(f(x)) )^{n+1} [o(x)o] ( g(f(x)) )^{[o(x)o](-1)}

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

... (1/(n+1))·( f(x) )^{n+1} [o(x)o] ( f(x) )^{[o(x)o](-1)}

int[ ( ax+b )^{n} ] d[x] = ...

... (1/(n+1))·( ax+b )^{n+1} [o(x)o] (1/a)

int[ ( e^{ax+b} )^{n} ] d[x] = ...

... (1/(n+1))·( e^{ax+b} )^{n+1} [o(x)o] (-1)·e^{(-1)·(ax+b)} [o(x)o] (-1)·(1/a^{2})

int[ ( ln( ax+b ) )^{n} ] d[x] = ...

... (1/(n+1))·( ln( ax+b ) )^{n+1} [o(x)o] ln( ln( ax+b ) ) [o(x)o] (1/3)·( ax+b )^{3} [o(x)o] (1/a^{3})

int[ ( sin(ax+b) )^{n} ] d[x] = ...

... (1/(n+1))·( sin(ax+b) )^{n+1} [o(x)o] sin(ax+b) [o(x)o] (1/a^{2})+...

... (1/(n+1))·( sin(ax+b) )^{n+1} [o(x)o] tan[o(x)o](ax+b) [o(x)o] (-1)·cos(ax+b) [o(x)o] (1/a^{3})

int[ ( cos(ax+b) )^{n} ] d[x] = ...

... (1/(n+1))·( cos(ax+b) )^{n+1} [o(x)o] cos(ax+b) [o(x)o] (1/a^{2})+...

... (1/(n+1))·( cos(ax+b) )^{n+1} [o(x)o] cot[o(x)o](ax+b) [o(x)o] (-1)·sin(ax+b) [o(x)o] (1/a^{3})

int[ (-1)·( sin(ax+b) )^{n} ] d[x] = ...

... (1/(n+1))·( sin(ax+b) )^{n+1} [o(x)o] (-1)·sin(ax+b) [o(x)o] (1/a^{2})+...

... (1/(n+1))·( sin(ax+b) )^{n+1} [o(x)o] tan[o(x)o](ax+b) [o(x)o] cos(ax+b) [o(x)o] (1/a^{3})

int[ (-1)·( cos(ax+b) )^{n} ] d[x] = ...

... (1/(n+1))·( cos(ax+b) )^{n+1} [o(x)o] (-1)·cos(ax+b) [o(x)o] (1/a^{2})+...

... (1/(n+1))·( cos(ax+b) )^{n+1} [o(x)o] cot[o(x)o](ax+b) [o(x)o] sin(ax+b) [o(x)o] (1/a^{3})

int[ ( sinh(ax+b) )^{n} ] d[x] = ...

... (1/(n+1))·( sinh(ax+b) )^{n+1} [o(x)o] sinh(ax+b) [o(x)o] (1/a^{2})+...

... (1/(n+1))·( sinh(ax+b) )^{n+1} [o(x)o] tanh[o(x)o](ax+b) [o(x)o] (-1)·cosh(ax+b) [o(x)o] (1/a^{3})

int[ (-1)·( cosh(ax+b) )^{n} ] d[x] = ...

... (1/(n+1))·( cosh(ax+b) )^{n+1} [o(x)o] cosh(ax+b) [o(x)o] (1/a^{2})+...

... (1/(n+1))·( cosh(ax+b) )^{n+1} [o(x)o] coth[o(x)o](ax+b) [o(x)o] (-1)·sinh(ax+b) [o(x)o] (1/a^{3})

int[ (-1)·( sinh(ax+b) )^{n} ] d[x] = ...

... (1/(n+1))·( sinh(ax+b) )^{n+1} [o(x)o] (-1)·sinh(ax+b) [o(x)o] (1/a^{2})+...

... (1/(n+1))·( sinh(ax+b) )^{n+1} [o(x)o] tanh[o(x)o](ax+b) [o(x)o] cosh(ax+b) [o(x)o] (1/a^{3})

int[ ( cosh(ax+b) )^{n} ] d[x] = ...

... (1/(n+1))·( cosh(ax+b) )^{n+1} [o(x)o] (-1)·cosh(ax+b) [o(x)o] (1/a^{2})+...

... (1/(n+1))·( cosh(ax+b) )^{n+1} [o(x)o] coth[o(x)o](ax+b) [o(x)o] sinh(ax+b) [o(x)o] (1/a^{3})

int[ ( 1/sin(x) ) ] d[x] = (-1)·cos(x)+cot[o(x)o](x) [o(x)o] sin(x)

int[ (-1)·( 1/cos(x) ) ] d[x] = (-1)·sin(x)+tan[o(x)o](x) [o(x)o] cos(x)

int[ ( 1/cos(x) ) ] d[x] = sin(x)+tan[o(x)o](x) [o(x)o] (-1)·cos(x)

int[ (-1)·( 1/sin(x) ) ] d[x] = cos(x)+cot[o(x)o](x) [o(x)o] (-1)·sin(x)

cinematica: tren de (-b) a b

d_{t}[x] = (a/(2b))·( x^{2}+(-1)·b^{2} )

( ( 1/(x+(-b)) )+(-1)( 1/(x+b) ) )·d_{t}[x] = a

ln(x+(-b))+(-1)·ln(x+b) = at

1+(-1)·( (2b)/(x+b) ) = e^{at}

( (2b)/(x+b) ) = 1+(-1)·e^{at}

x(t) = ( (2b)/(1+(-1)·e^{at}) )+(-b)

d_{t}[x] = (2ba)·( e^{at}/(1+(-1)·e^{at})^{2} )

cinemática: tren de zero a b

d_{t}[x] = (a/b)·x(x+(-b))

( ( 1/(x+(-b)) )+(-1)·(1/x) )·d_{t}[x] = a

ln(x+(-b))+(-1)·ln(x) = at

(1+(-1)(b/x)) = e^{at}

(b/x)  = 1+(-1)·e^{at}

x(t) = ( b/(1+(-1)·e^{at}) )

d_{t}[x] = (ba)·( e^{at}/(1+(-1)·e^{at})^{2} )

Teorema del Buey del Projimo

( x € Local ) <==> No ( y € Local )

( f( objeto ) € x ) <==> No ( f( objeto ) € y )

( x € Sucursal-de-Caixa-Bank ) <==> No ( y € Sucursal-de-Caixa-Bank )

( f( Marihuana ) € x ) <==> No ( f( Marihuana ) € y )

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})

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}}

ecuacions diferencials sinus-exponencial-potencial

d_{x}[ e[n]-sin-arc[m](x) ] = d_{x}[ x^{m}e^{nx}sin(x) ] = ...

... (1/x)·( m·e[n]-sin-arc[m](x)+nx·e[n]-sin-arc[m](x)+...

... x·( x^{2m}e^{2nx}+(-1)·( e[n]-sin-arc[m](x) )^{2} )^{(1/2)} )

d_{y}[ arc[m]-sin-e[n](y) ]  = ...

... arc[m]-sin-e[n](y)·( 1/( m·y+ny·arc[m]-sin-e[n](y)+...

... arc[m]-sin-e[n](y)·( ( arc[m]-sin-e[n](y) )^{2m}e^{2n·arc[m]-sin-e[n](y)}+(-1)·y^{2} )^{(1/2)} ) )

f(x) = (1/y)·( (m+ny)·e[n]-sin-arc[m](y)+y·e[n]-cos-arc[m](y) )·d_{x}[y]

int[ f(x) ] d[x] = y^{m}·e^{nx}·sin(y)

int[ f(x) ] d[x] = e[n]-sin-arc[m](y)

arc[m]-sin-e[n]( int[ f(x) ] d[x] ) = y(x)

ecuacions diferencials sinus-exponencial

d_{x}[ sin-e[n](x) ] = d_{x}[ e^{nx}·sin(x) ] = ...

... n·sin-e[n](x)+( e^{2nx}+(-1)·( sin-e[n](x) )^{2} )^{(1/2)}

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

... ( 1/( ny+( e^{2n·e[n]-sin(y)}+(-1)·y^{2} )^{(1/2)} ) )

f(x) = ( n·sin-e[n](y)+cos-e[n](y) )·d_{x}[y]

int[ f(x) ] d[x] = e^{ny}·sin(y)

int[ f(x) ] d[x] = sin-e[n](y)

e[n]-sin( int[ f(x) ] d[x] ) = y(x)

ecuacions diferencials sinus-potencia

d_{x}[ sin-arc[n](x) ] = d_{x}[ x^{n}·sin(x) ] = ...

... (1/x)·( n·sin-arc[n](x)+x·( x^{2n}+(-1)·( sin-arc[n](x) )^{2} )^{(1/2)} )

d_{y}[ arc[n]-sin(y) ] = ...

... arc[n]-sin(y)·( 1/( n·y+arc[n]-sin(y)·( ( arc[n]-sin(y) )^{2n}+(-1)·y^{2} )^{(1/2)} ) )

f(x) = (1/y)·( n·sin-arc[n](y)+y·cos-arc[n](y) )·d_{x}[y]

int[ f(x) ] d[x] = y^{n}·sin(y)

int[ f(x) ] d[x] = sin-arc[n](y)

arc[n]-sin( int[ f(x) ] d[x] ) = y(x)

mucho y poco

mucho [o] muchos

mucha [o] muchas

poco [o] pocos

poca [o] pocas

mult [o] mults

multa [o] multes

poc [o] pocs

poca [o] poques

multotzok [o] multotzoks

multotzak [o] multotzaks

pocotzok [o] pocotzoks

pocotzak [o] pocotzaks

mult-bicup-çí [o] mult-bicup-çís

mult-bicup-çuá [o] mult-bicup-çuás

poc-bicup-çí [o] poc-bicup-çís

poc-bicup-çuá [o] poc-bicup-cuás

és-de-puá mult-bicup-çí catalán.

és-de-puá poc-bicup-çí catalán.

verbos: moler y morir

ha muerto [o] está muerta

ha molido [o] está molida

ha mort [o] està morta

ha molit [o] està molida

ha-de-tek mortu-dut [o] està-de-tek morta-dat

ha-de-tek molitu-dut [o] està-de-tek molita-dat

ha-de-puá mortu-dom [ mort ] [o] està-de-puá morta-dam [ morta ]

ha-de-puá molitu-dom [ molit ] [o] està-de-puá molita-dam [ molita ]