Sr Examen
Ecuación diferencial sqrt(1-y^2)dx+y*(sqrt(1+x^2))dy=0
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Solución
Ha introducido
[src]
___________ ________
/ 2 / 2 d
\/ 1 - y (x) + \/ 1 + x *--(y(x))*y(x) = 0
dx
$$\sqrt{1 - y^{2}{\left(x \right)}} + \sqrt{x^{2} + 1} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
sqrt(1 - y^2) + sqrt(x^2 + 1)*y*y' = 0
Respuesta
[src]
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/ 2 2
y(x) = -\/ 1 - C1 - asinh (x) + 2*C1*asinh(x)
$$y{\left(x \right)} = - \sqrt{- C_{1}^{2} + 2 C_{1} \operatorname{asinh}{\left(x \right)} - \operatorname{asinh}^{2}{\left(x \right)} + 1}$$
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/ 2 2
y(x) = \/ 1 - C1 - asinh (x) + 2*C1*asinh(x)
$$y{\left(x \right)} = \sqrt{- C_{1}^{2} + 2 C_{1} \operatorname{asinh}{\left(x \right)} - \operatorname{asinh}^{2}{\left(x \right)} + 1}$$
Gráfico para el problema de Cauchy
Clasificación
separable
1st power series
lie group
separable Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.4121060758343621)
(-5.555555555555555, -2.787196876160507e-11)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 8.427456047434801e+197)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 7.40906269028575e-38)
(7.777777777777779, 8.388243566956694e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)