Sr Examen
Ecuación diferencial 2x(1-yy)dx-2y(1-xx)dy=0
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Solución
Ha introducido
[src]
2 d 2 d
2*x - 2*x*y (x) - 2*--(y(x))*y(x) + 2*x *--(y(x))*y(x) = 0
dx dx
$$2 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 2 x y^{2}{\left(x \right)} + 2 x - 2 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
2*x^2*y*y' - 2*x*y^2 + 2*x - 2*y*y' = 0
Respuesta
[src]
________________
/ 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
1st power series
lie group
separable Integral
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.8585367334626249)
(-5.555555555555555, 0.9316782521793422)
(-3.333333333333333, 0.9774032206338946)
(-1.1111111111111107, 0.9994815646451323)
(1.1111111111111107, 0.9994816569222176)
(3.333333333333334, 0.9774077361293774)
(5.555555555555557, 0.9316922061762314)
(7.777777777777779, 0.8585668566149796)
(10.0, 0.7500572095031366)
(10.0, 0.7500572095031366)