Sr Examen
Ecuación diferencial xy'y+2xy²=-y⁴
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Solución
Ha introducido
[src]
2 d 4
2*x*y (x) + x*--(y(x))*y(x) = -y (x)
dx
$$2 x y^{2}{\left(x \right)} + x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = - y^{4}{\left(x \right)}$$
2*x*y^2 + x*y*y' = -y^4
Respuesta
[src]
y(x) = 0
$$y{\left(x \right)} = 0$$
____________________
/ -4*x
___ / e
-\/ 2 * / ------------------
/ / pi*I\
\/ C1 + Ei\4*x*e /
y(x) = ----------------------------------
2
$$y{\left(x \right)} = - \frac{\sqrt{2} \sqrt{\frac{e^{- 4 x}}{C_{1} + \operatorname{Ei}{\left(4 x e^{i \pi} \right)}}}}{2}$$
____________________
/ -4*x
___ / e
\/ 2 * / ------------------
/ / pi*I\
\/ C1 + Ei\4*x*e /
y(x) = --------------------------------
2
$$y{\left(x \right)} = \frac{\sqrt{2} \sqrt{\frac{e^{- 4 x}}{C_{1} + \operatorname{Ei}{\left(4 x e^{i \pi} \right)}}}}{2}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
lie group
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.00893763341237981)
(-5.555555555555555, 0.00010495945882995557)
(-3.333333333333333, 1.2314223293710065e-06)
(-1.1111111111111107, 1.3992821874898813e-08)
(1.1111111111111107, -6.681985950227238e-11)
(3.333333333333334, -3.2970274216310637e-10)
(5.555555555555557, -5.0251251066044775e-11)
(7.777777777777779, -3.411706866810689e-11)
(10.0, -2.9090352921755416e-11)
(10.0, -2.9090352921755416e-11)