Sr Examen
Ecuación diferencial xydy-(x+1)sqrt(1-y^2)dx=0
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Solución
Ha introducido
[src]
___________ ___________
/ 2 / 2 d
- \/ 1 - y (x) - x*\/ 1 - y (x) + x*--(y(x))*y(x) = 0
dx
$$- x \sqrt{1 - y^{2}{\left(x \right)}} + x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - \sqrt{1 - y^{2}{\left(x \right)}} = 0$$
-x*sqrt(1 - y^2) + x*y*y' - sqrt(1 - y^2) = 0
Respuesta
[src]
____________________________________________________________
/ 2 2 2
y(x) = -\/ 1 - C1 - x - log (x) - 2*C1*x - 2*C1*log(x) - 2*x*log(x)
$$y{\left(x \right)} = - \sqrt{- C_{1}^{2} - 2 C_{1} x - 2 C_{1} \log{\left(x \right)} - x^{2} - 2 x \log{\left(x \right)} - \log{\left(x \right)}^{2} + 1}$$
____________________________________________________________
/ 2 2 2
y(x) = \/ 1 - C1 - x - log (x) - 2*C1*x - 2*C1*log(x) - 2*x*log(x)
$$y{\left(x \right)} = \sqrt{- C_{1}^{2} - 2 C_{1} x - 2 C_{1} \log{\left(x \right)} - x^{2} - 2 x \log{\left(x \right)} - \log{\left(x \right)}^{2} + 1}$$
Gráfico para el problema de Cauchy
Clasificación
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)