Sr Examen
Ecuación diferencial (xyy+x)dx+(y-xxy)dy=0
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Solución
Ha introducido
[src]
2 d 2 d
x + x*y (x) + --(y(x))*y(x) - x *--(y(x))*y(x) = 0
dx dx
$$- x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x y^{2}{\left(x \right)} + x + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
-x^2*y*y' + x*y^2 + x + y*y' = 0
Respuesta
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_________________
/ 2
y(x) = -\/ -1 - C1 + C1*x
$$y{\left(x \right)} = - \sqrt{C_{1} x^{2} - C_{1} - 1}$$
_________________
/ 2
y(x) = \/ -1 - C1 + C1*x
$$y{\left(x \right)} = \sqrt{C_{1} x^{2} - C_{1} - 1}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
Bernoulli
1st power series
lie group
separable Integral
1st exact Integral
Bernoulli Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -2.1732670805335713e-10)
(-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, 2.653805977506925e-32)
(7.777777777777779, 8.388243567719235e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)