Solving one equation with one unknown and get all possible solutions
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I have an equation and I need to get its solution. I think it has more than one solution, but using the command (solve) I can get only one solution.
Actually, it is expected to get real and complex solutions, but I am interested on the real solutions only.
How can I get this solution in Matlab.
the required unknown is (alphap) and my equation and the command that I have used is:
m=15; Ki=1.3908e+06; B=0.945e-1; db=0.79e-2; alphao=.2618;
x = solve(Pr == m*Ki*(B*db*(cos(alphao)/cos(alphap)-1))^(3/2)*sin(alphap),alphap)
The answer is:
x = 0.37336926931567958392238007768557i
Stephan on 4 Jan 2019
Edited: Stephan on 4 Jan 2019
getting all possible soultions is a hard job, because you have an infinite bunch of real solutions:
You find them for example by using fzero:
Pr = 10;
fun = @(alphap)Pr - m*Ki*(B*db*(cos(alphao)/cos(alphap)-1))^(3/2)*sin(alphap)
x1 = fzero(fun,0.5)
This code results in:
If you want more solutions just add or subtract integer multiples of 2*pi. Then you can construct as many real solutions as you want by yourself:
x2 = fzero(fun,2*pi+x1)
is_it_2_pi = (x2-x1)/(2*pi)