Solve a system of non linear equations with parameters

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Rakesh Jain
Rakesh Jain 2017-2-27
评论： Red_Devil_Box 2020-8-31
I have to find p11 p12 p22 in the following equations where q r b c are constants
p12^2/r + 2*c*p12 - 2*q = 0
p11 - b*p12 - c*p22 + (p12*p22)/r = 0
p22^2/r - 2*b*p22 + 2*p12 = 0
I specifically want to find p11 p12 and p22.
What should I do?

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Walter Roberson
Walter Roberson 2017-2-27
syms p12 r c q p11 b p22
eqns = [p12^2/r + 2*c*p12 - 2*q ==0, p11 - b*p12 - c*p22 + (p12*p22)/r == 0, p22^2/r - 2*b*p22 + 2*p12 == 0]
sol = solve(eqns, [p11 p12 p22])
P11 = simplify(sol.p11,'steps',20);
P12 = simplify(sol.p12,'steps',20);
P22 = simplify(sol.p12,'steps',20);
Note: there are 4 solutions for each variable.
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