Questions on (ordinary) differential equations. For questions specifically concerning partial differential equations, use the (pde) tag.

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Non linear second order ODE up to $O(\epsilon) $ for $v_{xx}-\left(v^{3}-v\right)-\varepsilon\frac{1}{2}\left(1-v^{2}\right)=0$

I really need help solving this : $$v_{xx}-\left(v^{3}-v\right)-\varepsilon\frac{1}{2}\left(1-v^{2}\right)=0 $$ With boundary conditions : $$ v(\pm \infty )=-1+\frac{1}{4}\epsilon $$ I need to ...