Sr Examen
Ecuación diferencial (2y^2lnx+y)dx+(xy+2xy(lnx)^2+xlnx)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
⌨
Solución
Ha introducido
[src]
2 d d 2 d
2*y (x)*log(x) + x*--(y(x))*log(x) + x*--(y(x))*y(x) + 2*x*log (x)*--(y(x))*y(x) + y(x) = 0
dx dx dx
$$2 x y{\left(x \right)} \log{\left(x \right)}^{2} \frac{d}{d x} y{\left(x \right)} + x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x \log{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + 2 y^{2}{\left(x \right)} \log{\left(x \right)} + y{\left(x \right)} = 0$$
2*x*y*log(x)^2*y' + x*y*y' + x*log(x)*y' + 2*y^2*log(x) + y = 0
Respuesta
[src]
_______________________________
/ 2 2
\/ log (x) + 2*C1 + 4*C1*log (x) - log(x)
y(x) = -------------------------------------------
2
1 + 2*log (x)
$$y{\left(x \right)} = \frac{\sqrt{4 C_{1} \log{\left(x \right)}^{2} + 2 C_{1} + \log{\left(x \right)}^{2}} - \log{\left(x \right)}}{2 \log{\left(x \right)}^{2} + 1}$$
/ _______________________________ \
| / 2 2 |
-\\/ log (x) + 2*C1 + 4*C1*log (x) + log(x)/
y(x) = -----------------------------------------------
2
1 + 2*log (x)
$$y{\left(x \right)} = - \frac{\sqrt{4 C_{1} \log{\left(x \right)}^{2} + 2 C_{1} + \log{\left(x \right)}^{2}} + \log{\left(x \right)}}{2 \log{\left(x \right)}^{2} + 1}$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, nan)
(-5.555555555555555, nan)
(-3.333333333333333, nan)
(-1.1111111111111107, nan)
(1.1111111111111107, nan)
(3.333333333333334, nan)
(5.555555555555557, nan)
(7.777777777777779, nan)
(10.0, nan)
(10.0, nan)