Solve a system of non linear equations with parameters

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?

Answer 1

[Walter Roberson]

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.

[Rakesh Jain]

Sir the code is not running Warning: The solutions are parametrized by the symbols: z = C_ z11 = C_

[Walter Roberson]

In sufficiently old MATLAB such as R2014a, you need to use

sol = solve(eqns, p11, p12, p22);

[Rakesh Jain]

Thank you. Got it

[Red_Devil_Box]

sir can u help me??