Sr Examen
Ecuación diferencial (x^2-4)ydy-x*sqrt(y^2+1)dx=0
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Solución
Ha introducido
[src]
___________
/ 2 d 2 d
- x*\/ 1 + y (x) - 4*--(y(x))*y(x) + x *--(y(x))*y(x) = 0
dx dx
$$x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - x \sqrt{y^{2}{\left(x \right)} + 1} - 4 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y*y' - x*sqrt(y^2 + 1) - 4*y*y' = 0
Respuesta
[src]
________________________________________________
/ 2/ 2\ 2 / 2\
-\/ -4 + log \-4 + x / + 4*C1 + 4*C1*log\-4 + x /
y(x) = -----------------------------------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{4 C_{1}^{2} + 4 C_{1} \log{\left(x^{2} - 4 \right)} + \log{\left(x^{2} - 4 \right)}^{2} - 4}}{2}$$
________________________________________________
/ 2/ 2\ 2 / 2\
\/ -4 + log \-4 + x / + 4*C1 + 4*C1*log\-4 + x /
y(x) = ---------------------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt{4 C_{1}^{2} + 4 C_{1} \log{\left(x^{2} - 4 \right)} + \log{\left(x^{2} - 4 \right)}^{2} - 4}}{2}$$
Gráfico para el problema de Cauchy
Clasificación
separable
1st exact
1st power series
lie group
separable Integral
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -1.0977027900273246e-08)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 4.1191008749990914e-33)
(7.777777777777779, 8.388243567719534e+296)
(10.0, 3.4850068345956685e-196)
(10.0, 3.4850068345956685e-196)