Ecuación diferencial xdx-ydy=yx^2dy-xy^2dx

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Ha introducido [src]

    d                    2       2 d            
x - --(y(x))*y(x) = - x*y (x) + x *--(y(x))*y(x)
    dx                             dx

$$x - y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} = x^{2} y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} - x y^{2}{\left(x \right)}$$

x - y*y' = x^2*y*y' - x*y^2

Respuesta [src]

           _________________
          /               2 
y(x) = -\/  -1 + C1 + C1*x

$$y{\left(x \right)} = - \sqrt{C_{1} x^{2} + C_{1} - 1}$$

          _________________
         /               2 
y(x) = \/  -1 + C1 + C1*x

$$y{\left(x \right)} = \sqrt{C_{1} x^{2} + C_{1} - 1}$$

Clasificación

factorable

separable

1st exact

Bernoulli

1st power series

lie group

separable Integral

1st exact Integral

Bernoulli Integral