# Domain of differential equation

I made some function for plotting Domain of differential equation , will show how it works for $$y'=\frac{\sqrt{1-x^2}}{\sqrt{1-y^2}}$$

g = Sqrt[1 - x^2];  h = Sqrt[1 - y^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],
ListPlot[sp, PlotStyle -> Directive[PointSize[Large], Red]]
]
];

PlotDomainDJSP[f, vars, ssp] Thats Domain of that Differential equation . I got few question.

(The idea why is not simple show region plot is because regionplot do not show that singular points are not in region , so i made some extra Listplot to show us it )

1. How i can make to make large space on Plot, for example if is Domain from -1

2. Can i make in that function also GeneralSolution=DSolve[...] ,so then plot that General Solution and finaly Show[ (all 3 (domain of d.e ,listpoint with singular points ,general solution] .

I cant DSolve[f,y[x],x] , because in $$f$$ is not y[x] (its y ) , if i try to change g=y[x]... or something like f=y[x]... my function for ploting will not work.

• Change f to f /. y -> y[x] inside DSolve – Michael E2 Nov 27 '18 at 13:10
• You think DSolve[{y'[x] == f /. y -> y[x]}, y[x], x] ? – Милош Вучковић Nov 27 '18 at 13:16
• Probably better with parentheses: DSolve[{y'[x] == (f /. y -> y[x])}, y[x], x] – Michael E2 Nov 27 '18 at 17:21
• Ye it works ,have you an idea for 1. question ? – Милош Вучковић Nov 27 '18 at 17:23
• PlotRange -> {{xmin, xmax}, {ymin, ymax}}? Look up PlotRangePadding, too. – Michael E2 Nov 27 '18 at 17:29