Sr Examen
Ecuación diferencial (1/y^2)dx+(1-2x/y^3)dy=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
d
2*x*--(y(x))
1 dx d
----- - ------------ + --(y(x)) = 0
2 3 dx
y (x) y (x)
$$- \frac{2 x \frac{d}{d x} y{\left(x \right)}}{y^{3}{\left(x \right)}} + \frac{d}{d x} y{\left(x \right)} + \frac{1}{y^{2}{\left(x \right)}} = 0$$
-2*x*y'/y^3 + y' + y^(-2) = 0
Respuesta
[src]
5 4 3 2
x 143*x 30*x 7*x 2*x / 6\
y(x) = C1 - --- - ------ - ----- - ---- - ---- + O\x /
2 14 11 8 5
C1 C1 C1 C1 C1
$$y{\left(x \right)} = - \frac{143 x^{5}}{C_{1}^{14}} - \frac{30 x^{4}}{C_{1}^{11}} - \frac{7 x^{3}}{C_{1}^{8}} - \frac{2 x^{2}}{C_{1}^{5}} - \frac{x}{C_{1}^{2}} + C_{1} + O\left(x^{6}\right)$$
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, 0.6630610772332834)
(-5.555555555555555, 0.5619964398580499)
(-3.333333333333333, 0.4368770413281411)
(-1.1111111111111107, 0.25356516157361336)
(1.1111111111111107, 0.1583530577730815)
(3.333333333333334, 0.2746360840983602)
(5.555555555555557, 0.35487594016588997)
(7.777777777777779, 0.4202061234348779)
(10.0, 0.4767751903671329)
(10.0, 0.4767751903671329)