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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}

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    And what then about, for example, $y=\cases{0&for $x\le 0$\\x^4/16&for $x\ge 0$}$?2012-02-27
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    The "general solution" to a differential equation is simply the set of all of its solutions. The set $S = \{y = (1/4 x^2 + c)^2 : c \text{ is a constant}\}$ is not the general solution to this differential equation, because $y = 0$ is a solution that is not in $S$.2012-02-27

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