Sr Examen
Ecuación diferencial sqrt(4+y^2)xdx+y(1+x^2)dy=0
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Solución
Ha introducido
[src]
___________
/ 2 d 2 d
x*\/ 4 + y (x) + --(y(x))*y(x) + x *--(y(x))*y(x) = 0
dx dx
$$x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x \sqrt{y^{2}{\left(x \right)} + 4} + y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = 0$$
x^2*y*y' + x*sqrt(y^2 + 4) + y*y' = 0
Respuesta
[src]
_______________________________________________
/ 2/ 2\ 2 / 2\
-\/ -16 + log \1 + x / + 4*C1 - 4*C1*log\1 + x /
y(x) = ----------------------------------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{4 C_{1}^{2} - 4 C_{1} \log{\left(x^{2} + 1 \right)} + \log{\left(x^{2} + 1 \right)}^{2} - 16}}{2}$$
_______________________________________________
/ 2/ 2\ 2 / 2\
\/ -16 + log \1 + x / + 4*C1 - 4*C1*log\1 + x /
y(x) = --------------------------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt{4 C_{1}^{2} - 4 C_{1} \log{\left(x^{2} + 1 \right)} + \log{\left(x^{2} + 1 \right)}^{2} - 16}}{2}$$
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, 1.2976510618648476)
(-5.555555555555555, 1.8328639863338687)
(-3.333333333333333, 2.493513556673174)
(-1.1111111111111107, 3.511982160357362)
(1.1111111111111107, 3.511982233369369)
(3.333333333333334, 2.4935127354333533)
(5.555555555555557, 1.8328631912287547)
(7.777777777777779, 1.2976499795852103)
(10.0, 0.7499980882818756)
(10.0, 0.7499980882818756)