Ecuación diferencial y'(x+y^2)=y

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Ha introducido [src]

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

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

(x + 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