Sr Examen
Ecuación diferencial (xy-x)^2dy+y(1-x)dx=0
El profesor se sorprenderá mucho al ver tu solución correcta😉
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Solución
Ha introducido
[src]
2 d 2 2 d 2 d x *--(y(x)) - x*y(x) + x *y (x)*--(y(x)) - 2*x *--(y(x))*y(x) + y(x) = 0 dx dx dx
$$x^{2} y^{2}{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - 2 x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x^{2} \frac{d}{d x} y{\left(x \right)} - x y{\left(x \right)} + y{\left(x \right)} = 0$$
x^2*y^2*y' - 2*x^2*y*y' + x^2*y' - x*y + y = 0
Respuesta
[src]
2 y (x) 1 ----- - - - log(x) - 2*y(x) + log(y(x)) = C1 2 x
$$\frac{y^{2}{\left(x \right)}}{2} - 2 y{\left(x \right)} - \log{\left(x \right)} + \log{\left(y{\left(x \right)} \right)} - \frac{1}{x} = C_{1}$$
Clasificación
separable
lie group
separable Integral