Sr Examen
Ecuación diferencial ydx=(x-2y^3)dy
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Solución
Ha introducido
[src]
d 3 d
y(x) = x*--(y(x)) - 2*y (x)*--(y(x))
dx dx
$$y{\left(x \right)} = x \frac{d}{d x} y{\left(x \right)} - 2 y^{3}{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$
y = x*y' - 2*y^3*y'
Respuesta
[src]
4 5 2 3
105*x 3*x 3*x x x / 6\
y(x) = C1 - -------- - ------ - ----- - ----- - ----- + O\x /
11 14 5 2 8
128*C1 2*C1 8*C1 2*C1 2*C1
$$y{\left(x \right)} = - \frac{3 x^{5}}{2 C_{1}^{14}} - \frac{105 x^{4}}{128 C_{1}^{11}} - \frac{x^{3}}{2 C_{1}^{8}} - \frac{3 x^{2}}{8 C_{1}^{5}} - \frac{x}{2 C_{1}^{2}} + C_{1} + O\left(x^{6}\right)$$
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, 0.5927212440139759)
(-5.555555555555555, 0.42884347488841523)
(-3.333333333333333, 0.2596408361414604)
(-1.1111111111111107, 0.08695231840226934)
(1.1111111111111107, -0.0869523884245162)
(3.333333333333334, -0.25964119857019924)
(5.555555555555557, -0.42884404345568017)
(7.777777777777779, -0.5927220028726252)
(10.0, -0.7500008986602142)
(10.0, -0.7500008986602142)