Sr Examen
Ecuación diferencial ydx−(x+6y^2)dy=0
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Solución
Ha introducido
[src]
d 2 d
- x*--(y(x)) - 6*y (x)*--(y(x)) + y(x) = 0
dx dx
$$- x \frac{d}{d x} y{\left(x \right)} - 6 y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} = 0$$
-x*y' - 6*y^2*y' + y = 0
Respuesta
[src]
4 2 3 5
5*x x x x 7*x / 6\
y(x) = C1 - -------- - ------ + ---- + ------- + -------- + O\x /
7 3 6*C1 5 9
1296*C1 36*C1 108*C1 3888*C1
$$y{\left(x \right)} = \frac{7 x^{5}}{3888 C_{1}^{9}} - \frac{5 x^{4}}{1296 C_{1}^{7}} + \frac{x^{3}}{108 C_{1}^{5}} - \frac{x^{2}}{36 C_{1}^{3}} + \frac{x}{6 C_{1}} + C_{1} + O\left(x^{6}\right)$$
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, 0.5310038453963473)
(-5.555555555555555, 0.35359166660471625)
(-3.333333333333333, 0.20043203658488123)
(-1.1111111111111107, 0.06366918040045882)
(1.1111111111111107, -0.061052530585592533)
(3.333333333333334, -0.17644507926095457)
(5.555555555555557, -0.28433243422006915)
(7.777777777777779, -0.38601260064196274)
(10.0, -0.4824476729577849)
(10.0, -0.4824476729577849)