Sr Examen
Ecuación diferencial (1-x^2)y'-xy-axy^2=0
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Solución
Ha introducido
[src]
/ 2\ d 2
\1 - x /*--(y(x)) - x*y(x) - a*x*y (x) = 0
dx
$$- a x y^{2}{\left(x \right)} - x y{\left(x \right)} + \left(1 - x^{2}\right) \frac{d}{d x} y{\left(x \right)} = 0$$
-a*x*y^2 - x*y + (1 - x^2)*y' = 0
Respuesta
[src]
______________
/ / 2\
\/ C1*\-1 + x / - C1
y(x) = ----------------------
/ 2\
a*\1 + C1 - x /
$$y{\left(x \right)} = \frac{- C_{1} + \sqrt{C_{1} \left(x^{2} - 1\right)}}{a \left(C_{1} - x^{2} + 1\right)}$$
______________
/ / 2\
C1 + \/ C1*\-1 + x /
y(x) = ----------------------
/ 2 \
a*\-1 + x - C1/
$$y{\left(x \right)} = \frac{C_{1} + \sqrt{C_{1} \left(x^{2} - 1\right)}}{a \left(- C_{1} + x^{2} - 1\right)}$$
Clasificación
factorable
separable
1st power series
lie group
separable Integral