Are Du Val singularities smoothable?

I am interested in when a Du Val surface singularity is smoothable. By Du Val singularity, I mean (the germ of a) isolated double point surface singularity admitting a resolution by blowups of isolated double points over the original. By smoothable, I mean when does there exist a flat family containing the singularity as one of the fibers, and a smooth germ as another fiber.

Any solution/reference would be appreciated.

Du Val singularities are indeed smoothable and, in fact, more is true: they are of class $$T$$, namely, they are quotient singularities admitting a $$1$$-parameter $$\mathbb{Q}$$-Gorenstein smoothing.
Du Val singularities are hypersurface singularities, hence they can be smoothed --- just replace the defining equation $$F(x,y,z) = 0$$ by the equation $$F(x,y,z) = \epsilon$$.