y-sin3x*y=x^3*e^((-1/3)cos3x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$- y \sin{\left(3 x \right)} + y = x^{3} e^{- \frac{\cos{\left(3 x \right)}}{3}}$$
Коэффициент при y равен
$$1 - \sin{\left(3 x \right)}$$
entonces son posibles los casos para x :
$$x < \frac{\pi}{6}$$
$$x = \frac{\pi}{6}$$
Consideremos todos los casos con detalles:
Con
$$x < \frac{\pi}{6}$$
la ecuación será
$$- y \cos{\left(3 \right)} + y - \frac{\left(-1 + \frac{\pi}{6}\right)^{3}}{e^{\frac{\sin{\left(3 \right)}}{3}}} = 0$$
su solución
$$y = \frac{\left(6 - \pi\right)^{3}}{216 \left(-1 + \cos{\left(3 \right)}\right) e^{\frac{\sin{\left(3 \right)}}{3}}}$$
Con
$$x = \frac{\pi}{6}$$
la ecuación será
$$- \frac{\pi^{3}}{216} = 0$$
su solución
no hay soluciones
/ -cos(3*x) \ / -cos(3*x) \
| ----------| | ----------|
| 3 3 | | 3 3 |
|x *e | |x *e |
y1 = - re|--------------| - I*im|--------------|
\-1 + sin(3*x) / \-1 + sin(3*x) /
$$y_{1} = - \operatorname{re}{\left(\frac{x^{3} e^{- \frac{\cos{\left(3 x \right)}}{3}}}{\sin{\left(3 x \right)} - 1}\right)} - i \operatorname{im}{\left(\frac{x^{3} e^{- \frac{\cos{\left(3 x \right)}}{3}}}{\sin{\left(3 x \right)} - 1}\right)}$$
y1 = -re(x^3*exp(-cos(3*x)/3)/(sin(3*x) - 1)) - i*im(x^3*exp(-cos(3*x)/3)/(sin(3*x) - 1))
Suma y producto de raíces
[src]
/ -cos(3*x) \ / -cos(3*x) \
| ----------| | ----------|
| 3 3 | | 3 3 |
|x *e | |x *e |
- re|--------------| - I*im|--------------|
\-1 + sin(3*x) / \-1 + sin(3*x) /
$$- \operatorname{re}{\left(\frac{x^{3} e^{- \frac{\cos{\left(3 x \right)}}{3}}}{\sin{\left(3 x \right)} - 1}\right)} - i \operatorname{im}{\left(\frac{x^{3} e^{- \frac{\cos{\left(3 x \right)}}{3}}}{\sin{\left(3 x \right)} - 1}\right)}$$
/ -cos(3*x) \ / -cos(3*x) \
| ----------| | ----------|
| 3 3 | | 3 3 |
|x *e | |x *e |
- re|--------------| - I*im|--------------|
\-1 + sin(3*x) / \-1 + sin(3*x) /
$$- \operatorname{re}{\left(\frac{x^{3} e^{- \frac{\cos{\left(3 x \right)}}{3}}}{\sin{\left(3 x \right)} - 1}\right)} - i \operatorname{im}{\left(\frac{x^{3} e^{- \frac{\cos{\left(3 x \right)}}{3}}}{\sin{\left(3 x \right)} - 1}\right)}$$
/ -cos(3*x) \ / -cos(3*x) \
| ----------| | ----------|
| 3 3 | | 3 3 |
|x *e | |x *e |
- re|--------------| - I*im|--------------|
\-1 + sin(3*x) / \-1 + sin(3*x) /
$$- \operatorname{re}{\left(\frac{x^{3} e^{- \frac{\cos{\left(3 x \right)}}{3}}}{\sin{\left(3 x \right)} - 1}\right)} - i \operatorname{im}{\left(\frac{x^{3} e^{- \frac{\cos{\left(3 x \right)}}{3}}}{\sin{\left(3 x \right)} - 1}\right)}$$
/ -cos(3*x) \ / -cos(3*x) \
| ----------| | ----------|
| 3 3 | | 3 3 |
|x *e | |x *e |
- re|--------------| - I*im|--------------|
\-1 + sin(3*x) / \-1 + sin(3*x) /
$$- \operatorname{re}{\left(\frac{x^{3} e^{- \frac{\cos{\left(3 x \right)}}{3}}}{\sin{\left(3 x \right)} - 1}\right)} - i \operatorname{im}{\left(\frac{x^{3} e^{- \frac{\cos{\left(3 x \right)}}{3}}}{\sin{\left(3 x \right)} - 1}\right)}$$
-re(x^3*exp(-cos(3*x)/3)/(-1 + sin(3*x))) - i*im(x^3*exp(-cos(3*x)/3)/(-1 + sin(3*x)))