Sr Examen
Ecuación diferencial 2xdx-ydy=yx*2dy-xy2dx
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Solución
Ha introducido
[src]
d 2 d
2*x - --(y(x))*y(x) = - x*y (x) + 2*x*--(y(x))*y(x)
dx dx
$$2 x - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = - x y^{2}{\left(x \right)} + 2 x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
2*x - y*y' = -x*y^2 + 2*x*y*y'
Respuesta
[src]
__________________
/ x
/ C1*e
y(x) = - / -2 + -----------
/ _________
\/ \/ 1 + 2*x
$$y{\left(x \right)} = - \sqrt{\frac{C_{1} e^{x}}{\sqrt{2 x + 1}} - 2}$$
__________________
/ x
/ C1*e
y(x) = / -2 + -----------
/ _________
\/ \/ 1 + 2*x
$$y{\left(x \right)} = \sqrt{\frac{C_{1} e^{x}}{\sqrt{2 x + 1}} - 2}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable
1st exact
Bernoulli
1st power series
lie group
separable Integral
1st exact Integral
Bernoulli Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 5.0016246939273)
(-5.555555555555555, 17.237039437548866)
(-3.333333333333333, 60.70422486947281)
(-1.1111111111111107, 270.6604001946925)
(1.1111111111111107, 401632.3280499997)
(3.333333333333334, 3.1933833808213433e-248)
(5.555555555555557, 1.5010063194974072e-76)
(7.777777777777779, 8.388243567354548e+296)
(10.0, 9.036991477623112e-277)
(10.0, 9.036991477623112e-277)