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