Sr Examen
Ecuación diferencial yx'+(y^3-x)y'=0
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Solución
Ha introducido
[src]
/ 3 \ d
\y (x) - x/*--(y(x)) + y(x) = 0
dx
$$\left(- x + y^{3}{\left(x \right)}\right) \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} = 0$$
(-x + y^3)*y' + y = 0
Respuesta
[src]
5 3 4 2
x 48*x 4*x 105*x 3*x / 6\
y(x) = C1 - --- - ----- - ---- - ------ - ----- + O\x /
2 14 8 11 5
C1 C1 C1 8*C1 2*C1
$$y{\left(x \right)} = - \frac{48 x^{5}}{C_{1}^{14}} - \frac{105 x^{4}}{8 C_{1}^{11}} - \frac{4 x^{3}}{C_{1}^{8}} - \frac{3 x^{2}}{2 C_{1}^{5}} - \frac{x}{C_{1}^{2}} + C_{1} + O\left(x^{6}\right)$$
Gráfico para el problema de Cauchy
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.588110841921366)
(-5.555555555555555, 0.4227508070837146)
(-3.333333333333333, 0.2547536962000362)
(-1.1111111111111107, 0.08510540279526177)
(1.1111111111111107, -0.08510944371032139)
(3.333333333333334, -0.2547653286624065)
(5.555555555555557, -0.422770535720881)
(7.777777777777779, -0.5881377580095778)
(10.0, -0.7500335430313079)
(10.0, -0.7500335430313079)