How can I select between two solutions?

Hello everyone,

I've been searching a solution for this problem but I haven't found anything that fits with it. I have the following equation:

dx=(y-x)(C1·y+C2)

I know the values of x, dx, c1 and c2 for 100 steps (x and dx are(100x1)vectors and c1 and c2 constants), so I solve the equation and I substitute those values, but this equation has two solutions for 'y'. I need the solution bounded by 0 and 1. How can I make Matlab to choose the solution I need? This is the code I use to get the two solutions:

sol= solve('dx=(y-x)*(y*C1+C2)')
for i=1:N
    dx=ACT_dot(i,1); x=ACT(i1,1)  % Set the dx and x values
    y_sol(i,1:2)=subs(sol)
end

As you can see 'y_sol' is a (Nx2) matrix where I store the two values. How can I make to chose the right value in each row?

Thanks for your your attention. Best Regards

Answer 1

[Ivan van der Kroon]

This is a standard quadratic formula, put it in the form

a*y^2+b*y+c=0

and the solutions are

y1=(-b+sqrt(b^2-4*a*c))/(2*a)
y2=(-b-sqrt(b^2-4*a*c))/(2*a)

now that you have both solutions, use operations like

 y=(y>=0)*(y<=1)*y;

but you probably have some continuity requirements that you want to implement. If you want to do it quickly for only 100 points I would suggest a for-loop with if-statements.