# Solution of d.e is out from Domain of d.e

$$y’=-\frac{\sqrt{1-y(x)^2}}{\sqrt{1-x^2}}$$

g = -Sqrt[1 - y^2];  h = Sqrt[1 - x^2]; f = g/h; vars = {x, y}; ssp1 = NSolve[{g == 0, h == 0}, vars]; ssp = Values[ssp1]; DomainDJ[f_, vars_] :=    RegionUnion[ImplicitRegion[FunctionDomain[f, vars], Evaluate@vars],     ImplicitRegion[FunctionDomain[1/f, vars], Evaluate@vars]];  PlotDomainDJSP[f_, vars_, sp_] := Module[{df}, spt = Transpose[sp];      df = DomainDJ[f, vars];     Show[         RegionPlot[df, PlotRange -> {{-2, 2}, {-2, 2}}],         ListPlot[sp, PlotStyle -> Directive[PointSize[Large], Red]]         ]                                         ];  PlotDomainDJSP[f, vars, ssp] 

This is my code to find domain of d.e

Now let’s solve that d.e

Opres = DSolve[-(Sqrt[1 - y[x]^2]/Sqrt[1 - x^2]) == y'[x], y[x], x]  {{y[x] -> -Sin[ArcSin[x] - C[1]]}} 

Now let’s plot General solution of d.e

Opresgraf =   Plot[Evaluate[y[x] /. Opres /. C[1] -> Range[-6, 6]], {x, -2, 2},    PlotRange -> 2]; 

Now General solution + Domain of d.e

Show[PlotDomainDJSP[f, vars, ssp], Opresgraf] 

Problem is here because particular Solution $$y=-x$$ going out from Domain of d.e.

$$y=-x$$ is solution but for $$x \in (-1,1)$$ .

My question is how i can plot a normal general solution with $$y=-x , x\in (-1,1)$$ but efective .