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Aug 31, 2014 at 20:27 vote accept mathcounterexamples.net
Aug 31, 2014 at 19:28 comment added Martin Hairer That makes it continuous to the right, but not to the left...
Aug 31, 2014 at 19:25 comment added mathcounterexamples.net Hello Martin, are you sure of your statement? Because for $x=0$ the equation has 2 solutions. The first one is the constant function equal to $0$ and the second one, the function equal to $0$ for $t < 0$ and to $\frac{t^2}{4}$ for $t \ge 0$. The solution of the differential equation seems continuous if you pick-up the second solution for $x=0$.
S Aug 31, 2014 at 19:06 history suggested Ali Caglayan CC BY-SA 3.0
modified $sign$ to $\operatorname{sign}$
Aug 31, 2014 at 18:55 review Suggested edits
S Aug 31, 2014 at 19:06
Aug 31, 2014 at 10:21 history answered Martin Hairer CC BY-SA 3.0