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xy+3y-2yx+4x+c la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
x*y + 3*y - 2*y*x + 4*x + c = 0
c+(4x+(−x2y+(xy+3y)))=0c + \left(4 x + \left(- x 2 y + \left(x y + 3 y\right)\right)\right) = 0
Simplificar
Solución detallada
Tenemos una ecuación lineal:
x*y+3*y-2*y*x+4*x+c = 0

Sumamos los términos semejantes en el miembro izquierdo de la ecuación:
c + 3*y + 4*x - x*y = 0

Move the summands with the other variables
del miembro izquierdo al derecho, obtenemos:
−xy+4x+3y=−c- x y + 4 x + 3 y = - c
Dividamos ambos miembros de la ecuación en (3*y + 4*x - x*y)/y
y = -c / ((3*y + 4*x - x*y)/y)

Obtenemos la respuesta: y = (c + 4*x)/(-3 + x)
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
c−xy+4x+3y=0c - x y + 4 x + 3 y = 0
Коэффициент при y равен
3−x3 - x
entonces son posibles los casos para x :
x<3x < 3
x=3x = 3
Consideremos todos los casos con detalles:
Con
x<3x < 3
la ecuación será
c+y+8=0c + y + 8 = 0
su solución
y=−c−8y = - c - 8
Con
x=3x = 3
la ecuación será
c+12=0c + 12 = 0
su solución
Gráfica
Suma y producto de raíces [src] 
suma
  /(-3 + re(x))*(4*im(x) + im(c))   (4*re(x) + re(c))*im(x)\   (-3 + re(x))*(4*re(x) + re(c))   (4*im(x) + im(c))*im(x)
I*|------------------------------ - -----------------------| + ------------------------------ + -----------------------
  |                2     2                       2     2   |                   2     2                       2     2   
  \    (-3 + re(x))  + im (x)        (-3 + re(x))  + im (x)/       (-3 + re(x))  + im (x)        (-3 + re(x))  + im (x)
i(−(re⁡(c)+4re⁡(x))im⁡(x)(re⁡(x)−3)2+(im⁡(x))2+(re⁡(x)−3)(im⁡(c)+4im⁡(x))(re⁡(x)−3)2+(im⁡(x))2)+(re⁡(c)+4re⁡(x))(re⁡(x)−3)(re⁡(x)−3)2+(im⁡(x))2+(im⁡(c)+4im⁡(x))im⁡(x)(re⁡(x)−3)2+(im⁡(x))2i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x\right)} - 3\right) \left(\operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(x\right)}\right)}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(x\right)}\right) \left(\operatorname{re}{\left(x\right)} - 3\right)}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} 
=
  /(-3 + re(x))*(4*im(x) + im(c))   (4*re(x) + re(c))*im(x)\   (-3 + re(x))*(4*re(x) + re(c))   (4*im(x) + im(c))*im(x)
I*|------------------------------ - -----------------------| + ------------------------------ + -----------------------
  |                2     2                       2     2   |                   2     2                       2     2   
  \    (-3 + re(x))  + im (x)        (-3 + re(x))  + im (x)/       (-3 + re(x))  + im (x)        (-3 + re(x))  + im (x)
i(−(re⁡(c)+4re⁡(x))im⁡(x)(re⁡(x)−3)2+(im⁡(x))2+(re⁡(x)−3)(im⁡(c)+4im⁡(x))(re⁡(x)−3)2+(im⁡(x))2)+(re⁡(c)+4re⁡(x))(re⁡(x)−3)(re⁡(x)−3)2+(im⁡(x))2+(im⁡(c)+4im⁡(x))im⁡(x)(re⁡(x)−3)2+(im⁡(x))2i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x\right)} - 3\right) \left(\operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(x\right)}\right)}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(x\right)}\right) \left(\operatorname{re}{\left(x\right)} - 3\right)}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} 
producto
  /(-3 + re(x))*(4*im(x) + im(c))   (4*re(x) + re(c))*im(x)\   (-3 + re(x))*(4*re(x) + re(c))   (4*im(x) + im(c))*im(x)
I*|------------------------------ - -----------------------| + ------------------------------ + -----------------------
  |                2     2                       2     2   |                   2     2                       2     2   
  \    (-3 + re(x))  + im (x)        (-3 + re(x))  + im (x)/       (-3 + re(x))  + im (x)        (-3 + re(x))  + im (x)
i(−(re⁡(c)+4re⁡(x))im⁡(x)(re⁡(x)−3)2+(im⁡(x))2+(re⁡(x)−3)(im⁡(c)+4im⁡(x))(re⁡(x)−3)2+(im⁡(x))2)+(re⁡(c)+4re⁡(x))(re⁡(x)−3)(re⁡(x)−3)2+(im⁡(x))2+(im⁡(c)+4im⁡(x))im⁡(x)(re⁡(x)−3)2+(im⁡(x))2i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x\right)} - 3\right) \left(\operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(x\right)}\right)}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(x\right)}\right) \left(\operatorname{re}{\left(x\right)} - 3\right)}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} 
=
I*((-3 + re(x))*(4*im(x) + im(c)) - (4*re(x) + re(c))*im(x)) + (-3 + re(x))*(4*re(x) + re(c)) + (4*im(x) + im(c))*im(x)
-----------------------------------------------------------------------------------------------------------------------
                                                             2     2                                                   
                                                 (-3 + re(x))  + im (x)
i(−(re⁡(c)+4re⁡(x))im⁡(x)+(re⁡(x)−3)(im⁡(c)+4im⁡(x)))+(re⁡(c)+4re⁡(x))(re⁡(x)−3)+(im⁡(c)+4im⁡(x))im⁡(x)(re⁡(x)−3)2+(im⁡(x))2\frac{i \left(- \left(\operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(x\right)}\right) \operatorname{im}{\left(x\right)} + \left(\operatorname{re}{\left(x\right)} - 3\right) \left(\operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(x\right)}\right)\right) + \left(\operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(x\right)}\right) \left(\operatorname{re}{\left(x\right)} - 3\right) + \left(\operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} 
(i*((-3 + re(x))*(4*im(x) + im(c)) - (4*re(x) + re(c))*im(x)) + (-3 + re(x))*(4*re(x) + re(c)) + (4*im(x) + im(c))*im(x))/((-3 + re(x))^2 + im(x)^2)
Respuesta rápida [src] 
       /(-3 + re(x))*(4*im(x) + im(c))   (4*re(x) + re(c))*im(x)\   (-3 + re(x))*(4*re(x) + re(c))   (4*im(x) + im(c))*im(x)
y1 = I*|------------------------------ - -----------------------| + ------------------------------ + -----------------------
       |                2     2                       2     2   |                   2     2                       2     2   
       \    (-3 + re(x))  + im (x)        (-3 + re(x))  + im (x)/       (-3 + re(x))  + im (x)        (-3 + re(x))  + im (x)
y1=i(−(re⁡(c)+4re⁡(x))im⁡(x)(re⁡(x)−3)2+(im⁡(x))2+(re⁡(x)−3)(im⁡(c)+4im⁡(x))(re⁡(x)−3)2+(im⁡(x))2)+(re⁡(c)+4re⁡(x))(re⁡(x)−3)(re⁡(x)−3)2+(im⁡(x))2+(im⁡(c)+4im⁡(x))im⁡(x)(re⁡(x)−3)2+(im⁡(x))2y_{1} = i \left(- \frac{\left(\operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{re}{\left(x\right)} - 3\right) \left(\operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(x\right)}\right)}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{\left(\operatorname{re}{\left(c\right)} + 4 \operatorname{re}{\left(x\right)}\right) \left(\operatorname{re}{\left(x\right)} - 3\right)}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{\left(\operatorname{im}{\left(c\right)} + 4 \operatorname{im}{\left(x\right)}\right) \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 3\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} 
y1 = i*(-(re(c) + 4*re(x))*im(x)/((re(x) - 3)^2 + im(x)^2) + (re(x) - 3)*(im(c) + 4*im(x))/((re(x) - 3)^2 + im(x)^2)) + (re(c) + 4*re(x))*(re(x) - 3)/((re(x) - 3)^2 + im(x)^2) + (im(c) + 4*im(x))*im(x)/((re(x) - 3)^2 + im(x)^2)
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