Ecuación diferencial xydx=(x^2+4y)dy

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Ha introducido [src]

          2 d            d            
x*y(x) = x *--(y(x)) + 4*--(y(x))*y(x)
            dx           dx

$$x y{\left(x \right)} = x^{2} \frac{d}{d x} y{\left(x \right)} + 4 y{\left(x \right)} \frac{d}{d x} y{\left(x \right)}$$

x*y = x^2*y' + 4*y*y'

Respuesta [src]

             2      4         
            x      x      / 6\
y(x) = C1 + -- - ----- + O\x /
            8    64*C1

$$y{\left(x \right)} = - \frac{x^{4}}{64 C_{1}} + \frac{x^{2}}{8} + C_{1} + O\left(x^{6}\right)$$

Clasificación

factorable

1st exact

1st power series

lie group

1st exact Integral