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- La ecuación:
- Ecuación x^2-49=0
-
Ecuación 1-x/2=x/3
-
Ecuación 3*x^2-9=0
-
Ecuación -8x-17=3x-105
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- -19*x+14*y=20
- 5*x-14*y=-15
- Derivada de:
-
e^(x^2)
- Límite de la función:
-
e^(x^2)
- Gráfico de la función y =:
-
e^(x^2)
-
Expresiones idénticas
- x.diff(x)- dos *x*y=e^(x^ dos)
- x.diff(x) menos 2 multiplicar por x multiplicar por y es igual a e en el grado (x al cuadrado )
- x.diff(x) menos dos multiplicar por x multiplicar por y es igual a e en el grado (x en el grado dos)
- x.diff(x)-2*x*y=e(x2)
- x.diffx-2*x*y=ex2
- x.diff(x)-2*x*y=e^(x²)
- x.diff(x)-2*x*y=e en el grado (x en el grado 2)
- x.diff(x)-2xy=e^(x^2)
- x.diff(x)-2xy=e(x2)
- x.diffx-2xy=ex2
- x.diffx-2xy=e^x^2
-
Expresiones semejantes
- x.diff(x)+2*x*y=e^(x^2)
x.diff(x)-2*x*y=e^(x^2) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
//x for 0 = 1\ / 2\ || | \x / |<1 for 1 = 1| - 2*x*y = E || | \\0 otherwise/
$$- 2 x y + \begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = e^{x^{2}}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$- 2 x y + \begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = e^{x^{2}}$$
Коэффициент при y равен
$$- 2 x$$
entonces son posibles los casos para x :
$$x < 0$$
$$x = 0$$
Consideremos todos los casos con detalles:
Con
$$x < 0$$
la ecuación será
$$2 y + \begin{cases} -1 & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} - e = 0$$
su solución
$$y = - \frac{1}{2} + \frac{e}{2}$$
Con
$$x = 0$$
la ecuación será
$$\begin{cases} 0 & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} - 1 = 0$$
su solución
cualquiera y
$$- 2 x y + \begin{cases} x & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} = e^{x^{2}}$$
Коэффициент при y равен
$$- 2 x$$
entonces son posibles los casos para x :
$$x < 0$$
$$x = 0$$
Consideremos todos los casos con detalles:
Con
$$x < 0$$
la ecuación será
$$2 y + \begin{cases} -1 & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} - e = 0$$
su solución
$$y = - \frac{1}{2} + \frac{e}{2}$$
Con
$$x = 0$$
la ecuación será
$$\begin{cases} 0 & \text{for}\: 0 = 1 \\1 & \text{for}\: 1 = 1 \\0 & \text{otherwise} \end{cases} - 1 = 0$$
su solución
cualquiera y
Gráfica
Respuesta rápida
[src]
/ / 2 2 \ 2 2 \ / 2 2 \ 2 2
| | re (x) - im (x)| re (x) - im (x) | | re (x) - im (x)| re (x) - im (x)
| \1 - cos(2*im(x)*re(x))*e /*im(x) e *re(x)*sin(2*im(x)*re(x))| \1 - cos(2*im(x)*re(x))*e /*re(x) e *im(x)*sin(2*im(x)*re(x))
y1 = I*|- ----------------------------------------------- - -----------------------------------------| + ----------------------------------------------- - -----------------------------------------
| / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \
\ 2*\im (x) + re (x)/ 2*\im (x) + re (x)/ / 2*\im (x) + re (x)/ 2*\im (x) + re (x)/
$$y_{1} = \frac{\left(- e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} + 1\right) \operatorname{re}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)} + i \left(- \frac{\left(- e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} + 1\right) \operatorname{im}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)} - \frac{e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} \operatorname{re}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}\right) - \frac{e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} \operatorname{im}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}$$
y1 = (-exp(re(x)^2 - im(x)^2)*cos(2*re(x)*im(x)) + 1)*re(x)/(2*(re(x)^2 + im(x)^2)) + i*(-(-exp(re(x)^2 - im(x)^2)*cos(2*re(x)*im(x)) + 1)*im(x)/(2*(re(x)^2 + im(x)^2)) - exp(re(x)^2 - im(x)^2)*sin(2*re(x)*im(x))*re(x)/(2*(re(x)^2 + im(x)^2))) - exp(re(x)^2 - im(x)^2)*sin(2*re(x)*im(x))*im(x)/(2*(re(x)^2 + im(x)^2))
Suma y producto de raíces
[src]
suma
/ / 2 2 \ 2 2 \ / 2 2 \ 2 2 | | re (x) - im (x)| re (x) - im (x) | | re (x) - im (x)| re (x) - im (x) | \1 - cos(2*im(x)*re(x))*e /*im(x) e *re(x)*sin(2*im(x)*re(x))| \1 - cos(2*im(x)*re(x))*e /*re(x) e *im(x)*sin(2*im(x)*re(x)) I*|- ----------------------------------------------- - -----------------------------------------| + ----------------------------------------------- - ----------------------------------------- | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \ 2*\im (x) + re (x)/ 2*\im (x) + re (x)/ / 2*\im (x) + re (x)/ 2*\im (x) + re (x)/
$$\frac{\left(- e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} + 1\right) \operatorname{re}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)} + i \left(- \frac{\left(- e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} + 1\right) \operatorname{im}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)} - \frac{e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} \operatorname{re}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}\right) - \frac{e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} \operatorname{im}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}$$
=
/ / 2 2 \ 2 2 \ / 2 2 \ 2 2 | | re (x) - im (x)| re (x) - im (x) | | re (x) - im (x)| re (x) - im (x) | \1 - cos(2*im(x)*re(x))*e /*im(x) e *re(x)*sin(2*im(x)*re(x))| \1 - cos(2*im(x)*re(x))*e /*re(x) e *im(x)*sin(2*im(x)*re(x)) I*|- ----------------------------------------------- - -----------------------------------------| + ----------------------------------------------- - ----------------------------------------- | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \ 2*\im (x) + re (x)/ 2*\im (x) + re (x)/ / 2*\im (x) + re (x)/ 2*\im (x) + re (x)/
$$\frac{\left(- e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} + 1\right) \operatorname{re}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)} + i \left(- \frac{\left(- e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} + 1\right) \operatorname{im}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)} - \frac{e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} \operatorname{re}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}\right) - \frac{e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} \operatorname{im}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}$$
producto
/ / 2 2 \ 2 2 \ / 2 2 \ 2 2 | | re (x) - im (x)| re (x) - im (x) | | re (x) - im (x)| re (x) - im (x) | \1 - cos(2*im(x)*re(x))*e /*im(x) e *re(x)*sin(2*im(x)*re(x))| \1 - cos(2*im(x)*re(x))*e /*re(x) e *im(x)*sin(2*im(x)*re(x)) I*|- ----------------------------------------------- - -----------------------------------------| + ----------------------------------------------- - ----------------------------------------- | / 2 2 \ / 2 2 \ | / 2 2 \ / 2 2 \ \ 2*\im (x) + re (x)/ 2*\im (x) + re (x)/ / 2*\im (x) + re (x)/ 2*\im (x) + re (x)/
$$\frac{\left(- e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} + 1\right) \operatorname{re}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)} + i \left(- \frac{\left(- e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} + 1\right) \operatorname{im}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)} - \frac{e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} \operatorname{re}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}\right) - \frac{e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} \operatorname{im}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}$$
=
// 2 2 \ 2 2 \ / 2 2 \ 2 2
|| re (x) - im (x)| re (x) - im (x) | | re (x) - im (x)| re (x) - im (x)
I*\\-1 + cos(2*im(x)*re(x))*e /*im(x) - e *re(x)*sin(2*im(x)*re(x))/ - \-1 + cos(2*im(x)*re(x))*e /*re(x) - e *im(x)*sin(2*im(x)*re(x))
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2 2 \
2*\im (x) + re (x)/
$$\frac{i \left(\left(e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} - 1\right) \operatorname{im}{\left(x\right)} - e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} \operatorname{re}{\left(x\right)}\right) - \left(e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} - 1\right) \operatorname{re}{\left(x\right)} - e^{\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(2 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)} \right)} \operatorname{im}{\left(x\right)}}{2 \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)}$$
(i*((-1 + cos(2*im(x)*re(x))*exp(re(x)^2 - im(x)^2))*im(x) - exp(re(x)^2 - im(x)^2)*re(x)*sin(2*im(x)*re(x))) - (-1 + cos(2*im(x)*re(x))*exp(re(x)^2 - im(x)^2))*re(x) - exp(re(x)^2 - im(x)^2)*im(x)*sin(2*im(x)*re(x)))/(2*(im(x)^2 + re(x)^2))