sqrt(4) gives 2 in CAS systems, since the principal root is returned by default.
Is there an option to have Maple return all roots? Which in this case 2,-2?
I'll explain the context why I need this.
When I solve an ODE, I get a solution that I need to solve for constant of integration C from initial conditions. For an example assume the ODE becomes, after replacing initial condition the following eq:=4^(1/2) = -2+_C1;
So now when solving for _C1 in maple and then calling simplify, gives one solution which _C1=4 (case root=2) which when replaced back into the general solution gives the particular solution.
But this means the second solution is lost, which is when _C1=0 (case root=-2) which could have been obtained from the non-principal root of 4^(1/2)
eq:=4^(1/2) = -2+_C; solve(eq,_C);
gives
And I would like to get {4,0} instead.
In practice, this becomes important.
Here is an actual ODE, which should have 2 solutions. Mathematica gives both solutions, and Maple gives one solution. This is due to the above.
ode:=diff(y(x),x)-y(x)=x*y(x)^(1/2); ic:=y(0)=4; dsolve([ode,ic])
In Mathematica
ode=y'[x]-y[x]==x*y[x]^(1/2); ic={y[0]==4}; sol=DSolve[{ode,ic},y[x],x]
The second solution above came from when constant of integration is zero. The first solution is the one Maple gave (when expanded).
When I worked the solution by hand, I tracked this to issue with sqrt(4) giving 2 and not +2,-2 when doing solve() to solve for C at the end.
I could ofcourse leave C=sqrt(4) and not call simplify on it and that works.
But I thought to ask here to see if there is some option in Maple, so that when it sees (n)^m to return all m roots when calling solve() and not just the principal one. Even for m=2.
I looked at root and tried allsolutions=true but they did not help. Looked at solve/details and did not spot something. I tried only few of the options there, as there are so many.
Any suggestions what to try?