Sr Examen
Ecuación diferencial ydx+(x-(1/2)*x^(3)*y)dy=0
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Solución
Ha introducido
[src]
3 d
x *--(y(x))*y(x)
d dx
x*--(y(x)) - ---------------- + y(x) = 0
dx 2
$$- \frac{x^{3} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}}{2} + x \frac{d}{d x} y{\left(x \right)} + y{\left(x \right)} = 0$$
-x^3*y*y'/2 + x*y' + y = 0
Respuesta
[src]
_________________
/ / 2\
C1 \/ C1*\-4 + C1*x /
y(x) = -- - --------------------
2 2*x
$$y{\left(x \right)} = \frac{C_{1}}{2} - \frac{\sqrt{C_{1} \left(C_{1} x^{2} - 4\right)}}{2 x}$$
_________________
/ / 2\
C1 \/ C1*\-4 + C1*x /
y(x) = -- + --------------------
2 2*x
$$y{\left(x \right)} = \frac{C_{1}}{2} + \frac{\sqrt{C_{1} \left(C_{1} x^{2} - 4\right)}}{2 x}$$
Gráfico para el problema de Cauchy
Clasificación
factorable
separable reduced
lie group
separable reduced Integral
Respuesta numérica
[src]
(x, y):
(-10.0, 0.75)
(-7.777777777777778, 0.7432284232433654)
(-5.555555555555555, 0.7262218596842167)
(-3.333333333333333, 0.655818977792018)
(-1.1111111111111107, 0.38006682981982287)
(1.1111111111111107, 8.894869667588977e+252)
(3.333333333333334, 9.083672372605533e+223)
(5.555555555555557, 6.94434051387447e-310)
(7.777777777777779, 6.94444627791123e-310)
(10.0, 1.1891235047637943e+292)
(10.0, 1.1891235047637943e+292)