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?: $\begin{aligned} y= \left(\frac {1}{4}x^2+c \right)^2 \end{aligned}$