This ode
ode:=diff(y(x),x)=sqrt(1-y(x)^2)
has general solution y(x) = sin(x + _C1) but it also has solution y=-1 and y=+1. Since these extra solutions can't be obtained from the general solution by specific value of the constant of integration, they are singular solution.
But I am not able to get Maple to show these:
restart;
ode:=diff(y(x),x)=sqrt(1-y(x)^2);
dsolve(ode);
dsolve(ode,'singsol'='all',[separable]);
dsolve(ode,[separable]);
We can check that y=1.,y=-1 are solutions
odetest(y(x)=1,ode);
odetest(y(x)=-1,ode);
0
0
Only after I used this, was Maple able to gives these solutions
dsolve(ode,'Lie');
dsolve(ode,'Lie',singsol=all);
So only when using `Lie` symmetry methods and also using singsol=all it worked.
Most people will not think of using this specialized option.
Why Maple did not give these singular solutions using the standard dsolve(ode,singsol=all) command?
Should it not have done so? Now it makes it more confusing as to which option to use to obtain the singular solution, as one might have to keep trying different options.
What do others think?
Maple 2020.2