Sr Examen
Ecuación diferencial (x+y)dy+(ylny-2xy)dx=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d d x*--(y(x)) + --(y(x))*y(x) + log(y(x))*y(x) - 2*x*y(x) = 0 dx dx
$$- 2 x y{\left(x \right)} + x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} \log{\left(y{\left(x \right)} \right)} + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
-2*x*y + x*y' + y*log(y) + y*y' = 0
Respuesta
[src]
/ C1\
| x + --|
| x |
|e |
y(x) = x*W|-------|
\ x /
$$y{\left(x \right)} = x W\left(\frac{e^{\frac{C_{1}}{x} + x}}{x}\right)$$
Gráfico para el problema de Cauchy
Clasificación
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 9.225018023558428)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 8.973398002470273e-67)
(7.777777777777779, 8.388243567720288e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)