Ecuación diferencial y(x+y)dx+(xy+1)dy=0

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Ha introducido [src]

 2                 d               d           
y (x) + x*y(x) + x*--(y(x))*y(x) + --(y(x)) = 0
                   dx              dx

$$x y{\left(x \right)} \frac{d}{d x} y{\left(x \right)} + x y{\left(x \right)} + y^{2}{\left(x \right)} + \frac{d}{d x} y{\left(x \right)} = 0$$

x*y*y' + x*y + y^2 + y' = 0

Respuesta [src]

        /         ______\
        |        /    2 |
        |       /   -x  |
       W\C1*x*\/   e    /
y(x) = ------------------
               x

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

Clasificación

1st exact

1st power series

lie group

1st exact Integral