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- La ecuación:
-
Ecuación x^2-11*x+30=0
- Ecuación x^2+y^2=9
-
Ecuación -33-y=-19
-
Ecuación 11/(x-9)=-10
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -4*x+6*y=-7
- -7*x-13*y=5
- -18*x+8*y=-2
- Integral de d{x}:
- lny
- Derivada de:
-
lny
-
Expresiones idénticas
- lny=ax+by
- lny es igual a ax más by
-
Expresiones semejantes
- a*x+b*y+c=0
- a*x+b*y-82/9=0
- ln(y/(sqrt(y^2+1)))=lnx+C
- x^2+5xy+y^2*ln(y/x)=0
- lny=ax-by
-
Expresiones con funciones
- lny
- lny=t
- lny=(-1/x)+lnc
- lny+(x/y)^0.5=2
- ax
- ax+by+c=0
- ax=-by-c
- ax+√(3-2x-x^2)=4a+2
- ax^2=c
- ax+b-b=c-b
lny=ax+by la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$\log{\left(y \right)} = a x + b y$$
Коэффициент при x равен
$$- a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$- b y + x + \log{\left(y \right)} = 0$$
su solución
$$x = b y - \log{\left(y \right)}$$
Con
$$a = 0$$
la ecuación será
$$- b y + \log{\left(y \right)} = 0$$
su solución
$$\log{\left(y \right)} = a x + b y$$
Коэффициент при x равен
$$- a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$- b y + x + \log{\left(y \right)} = 0$$
su solución
$$x = b y - \log{\left(y \right)}$$
Con
$$a = 0$$
la ecuación será
$$- b y + \log{\left(y \right)} = 0$$
su solución
Gráfica
Suma y producto de raíces
[src]
suma
/(-im(b*y) + arg(y))*re(a) (-re(b*y) + log(|y|))*im(a)\ (-im(b*y) + arg(y))*im(a) (-re(b*y) + log(|y|))*re(a) I*|------------------------- - ---------------------------| + ------------------------- + --------------------------- | 2 2 2 2 | 2 2 2 2 \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(- \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
/(-im(b*y) + arg(y))*re(a) (-re(b*y) + log(|y|))*im(a)\ (-im(b*y) + arg(y))*im(a) (-re(b*y) + log(|y|))*re(a) I*|------------------------- - ---------------------------| + ------------------------- + --------------------------- | 2 2 2 2 | 2 2 2 2 \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(- \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
producto
/(-im(b*y) + arg(y))*re(a) (-re(b*y) + log(|y|))*im(a)\ (-im(b*y) + arg(y))*im(a) (-re(b*y) + log(|y|))*re(a) I*|------------------------- - ---------------------------| + ------------------------- + --------------------------- | 2 2 2 2 | 2 2 2 2 \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$i \left(- \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
=
(-re(b*y) + log(|y|))*re(a) - I*((-arg(y) + im(b*y))*re(a) + (-re(b*y) + log(|y|))*im(a)) - (-arg(y) + im(b*y))*im(a)
---------------------------------------------------------------------------------------------------------------------
2 2
im (a) + re (a)
$$\frac{- i \left(\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)} + \left(\operatorname{im}{\left(b y\right)} - \arg{\left(y \right)}\right) \operatorname{re}{\left(a\right)}\right) + \left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(b y\right)} - \arg{\left(y \right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
((-re(b*y) + log(|y|))*re(a) - i*((-arg(y) + im(b*y))*re(a) + (-re(b*y) + log(|y|))*im(a)) - (-arg(y) + im(b*y))*im(a))/(im(a)^2 + re(a)^2)
Respuesta rápida
[src]
/(-im(b*y) + arg(y))*re(a) (-re(b*y) + log(|y|))*im(a)\ (-im(b*y) + arg(y))*im(a) (-re(b*y) + log(|y|))*re(a)
x1 = I*|------------------------- - ---------------------------| + ------------------------- + ---------------------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$x_{1} = i \left(- \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\log{\left(\left|{y}\right| \right)} - \operatorname{re}{\left(b y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(- \operatorname{im}{\left(b y\right)} + \arg{\left(y \right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x1 = i*(-(log(|y|) - re(b*y))*im(a)/(re(a)^2 + im(a)^2) + (-im(b*y) + arg(y))*re(a)/(re(a)^2 + im(a)^2)) + (log(|y|) - re(b*y))*re(a)/(re(a)^2 + im(a)^2) + (-im(b*y) + arg(y))*im(a)/(re(a)^2 + im(a)^2)