Sr Examen
Ecuación diferencial (y^2)ln(x)dx-(y-1)(x)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d 2 d x*--(y(x)) + y (x)*log(x) - x*--(y(x))*y(x) = 0 dx dx
$$- x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x \frac{d}{d x} y{\left(x \right)} + y^{2}{\left(x \right)} \log{\left(x \right)} = 0$$
-x*y*y' + x*y' + y^2*log(x) = 0
Respuesta
[src]
/ ___________ \
2 | / 2 |
log (x) | / -log (x) -C1|
C1 + ------- + W\-\/ e *e /
2
y(x) = e
$$y{\left(x \right)} = e^{C_{1} + \frac{\log{\left(x \right)}^{2}}{2} + W\left(- e^{- C_{1}} \sqrt{e^{- \log{\left(x \right)}^{2}}}\right)}$$
/ ___________ \
2 | / 2 |
log (x) | / -log (x) -C1|
C1 + ------- + W\\/ e *e /
2
y(x) = e
$$y{\left(x \right)} = e^{C_{1} + \frac{\log{\left(x \right)}^{2}}{2} + W\left(e^{- C_{1}} \sqrt{e^{- \log{\left(x \right)}^{2}}}\right)}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
lie group
separable 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)