Ecuación diferencial dxxy^2-dyy=-dxx+dyx^2y

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Ha introducido [src]

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

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

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

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

Ecuación diferencial dx*x*y^2-dy*y=-dx*x+dy*x^2*y