Sr Examen
Ecuación diferencial sqrt5+y^2+yy'sqrt1-x^2
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Solución
Ha introducido
[src]
___ 2 2 d
\/ 5 + y (x) - x + --(y(x))*y(x) = 0
dx
$$- x^{2} + y^{2}{\left(x \right)} + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + \sqrt{5} = 0$$
-x^2 + y^2 + y*y' + sqrt(5) = 0
Respuesta
[src]
_____________________________________
/ ___ 2 -2*x
-\/ 2 - 4*x - 4*\/ 5 + 4*x + C1*e
y(x) = ------------------------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{C_{1} e^{- 2 x} + 4 x^{2} - 4 x - 4 \sqrt{5} + 2}}{2}$$
_____________________________________
/ ___ 2 -2*x
\/ 2 - 4*x - 4*\/ 5 + 4*x + C1*e
y(x) = ----------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt{C_{1} e^{- 2 x} + 4 x^{2} - 4 x - 4 \sqrt{5} + 2}}{2}$$
Gráfico para el problema de Cauchy
Clasificación
Bernoulli
almost linear
1st power series
lie group
Bernoulli Integral
almost linear Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 8.079030426101786)
(-5.555555555555555, 5.888024436992948)
(-3.333333333333333, 3.564856485146842)
(-1.1111111111111107, 0.7807740691973091)
(1.1111111111111107, 8.935705442103392e-09)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 3.4667248631491264e+179)
(7.777777777777779, 8.388243567736269e+296)
(10.0, 3.861029683e-315)
(10.0, 3.861029683e-315)