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Sep 21, 2017 at 2:56 comment added Rajesh D @LoïcTeyssier : Agree. Can you please look at my attempt below.
Sep 20, 2017 at 3:02 answer added Rajesh D timeline score: -1
Sep 19, 2017 at 20:09 comment added Loïc Teyssier Noticing that $|u|u=\pm u^2$, you can solve by quadrature your equations by incorporating the $\pm$ sign in the $\lambda$ on intervals over which the respective function $u$ and its derivative don't vanish. You obtain something defined implicitly as $F(u(x))=d+x$ where $\frac{dF}{du}=(c+0.5\lambda u^3)^{-1/3}$ for two constants $c, d$ whose value is given by the initial values you provide. Don't know if that helps, though.
Sep 19, 2017 at 15:53 history edited Rajesh D CC BY-SA 3.0
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Sep 19, 2017 at 12:14 history edited Rajesh D CC BY-SA 3.0
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Sep 19, 2017 at 7:45 history asked Rajesh D CC BY-SA 3.0