Ecuación diferencial (x+y^2)dy=ydx

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Ha introducido [src]

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

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

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

Respuesta [src]

               ___________
              /   2       
       C1   \/  C1  + 4*x 
y(x) = -- - --------------
       2          2

$$y{\left(x \right)} = \frac{C_{1}}{2} - \frac{\sqrt{C_{1}^{2} + 4 x}}{2}$$

               ___________
              /   2       
       C1   \/  C1  + 4*x 
y(x) = -- + --------------
       2          2

$$y{\left(x \right)} = \frac{C_{1}}{2} + \frac{\sqrt{C_{1}^{2} + 4 x}}{2}$$

Clasificación

1st exact

1st power series

lie group

1st exact Integral