Is a differential equation still having a general solution even if the differential equation have a singular solution?
for example:
\begin{aligned} \frac {dy}{dx} = x y^{1/2} \end{aligned}
The Solution: \begin{aligned} y= \left(\frac {1}{4}x^2+c \right)^2 \end{aligned}
But also this singular solution (there is not a constant to obtain it from the above, but is a solution) \begin{aligned} y= 0 \end{aligned}
Is this function correct named as a general solution?: \begin{aligned} y= \left(\frac {1}{4}x^2+c \right)^2 \end{aligned}