Sr Examen
Ecuación diferencial dx/y-(x+y^2)/y^2*dy=0
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Solución
Ha introducido
[src]
d
x*--(y(x))
1 d dx
---- - --(y(x)) - ---------- = 0
y(x) dx 2
y (x)
$$- \frac{x \frac{d}{d x} y{\left(x \right)}}{y^{2}{\left(x \right)}} - \frac{d}{d x} y{\left(x \right)} + \frac{1}{y{\left(x \right)}} = 0$$
-x*y'/y^2 - y' + 1/y = 0
Respuesta
[src]
2 4 3 5
x x 5*x 2*x 14*x / 6\
y(x) = C1 + -- - --- - ---- + ---- + ----- + O\x /
C1 3 7 5 9
C1 C1 C1 C1
$$y{\left(x \right)} = \frac{14 x^{5}}{C_{1}^{9}} - \frac{5 x^{4}}{C_{1}^{7}} + \frac{2 x^{3}}{C_{1}^{5}} - \frac{x^{2}}{C_{1}^{3}} + \frac{x}{C_{1}} + C_{1} + O\left(x^{6}\right)$$
Clasificación
factorable
1st exact
1st power series
lie group
1st exact Integral