MATLAB: Solve-Unable to find explicit solution

rewritesolve

Hi there,

I am tring to use the solve function to solve a pretty long equation but the system shoot me the warning that cannot find a explicit solution

clc,clear
syms A X Y E R n F M p
eq = p == (M*(exp(-A/X) - 1) - (exp(-A/X)*(M*(exp((A - R + E*n)/X) - 1)...
    + exp((A - R + E*n)/X)*((M*(exp(-E/X) - 1)*((exp(-E/X)*cos((pi*F)/180))^n - 1))...
    /(exp(-E/X)*cos((pi*F)/180) - 1) + M*exp(-(E*n)/X)*cos((pi*F)/180)...
    ^n*(exp(-A/X) - 1))))/(exp(-R/X)*cos((pi*F)/180)^n + 1))/(M*(exp(-A/Y) - 1)...
    - (exp(-A/Y)*(M*(exp((A - R + E*n)/Y) - 1) + exp((A - R + E*n)/Y)...
    *((M*(exp(-E/Y) - 1)*((exp(-E/Y)*cos((pi*F)/180))^n - 1))...
    /(exp(-E/Y)*cos((pi*F)/180) - 1) + M*exp(-(E*n)/Y)...
    *cos((pi*F)/180)^n*(exp(-A/Y) - 1))))/(exp(-R/Y)*cos((pi*F)/180)^n + 1));
Q = rewrite(eq,'sincos')
solution = solve(Q,X)

I tried to rewirte the whole equation into trigonometric terms but still cannot solve this equation. My MATLAB version is R2018b

What else can I try?

Best Answer

I think you can't find symbolical expression/solution for this equation. It's too complicated

Define all known constants/variables and use numerical approach (vpasolve or fsolve)

Related Solutions

MATLAB: Solving symbolic trig equation

You can NEVER solve for those variables, at least as the equations are written.

First of all, z never even appears. But since you never try to solve for it, who cares?

But look at x + y. They always appear tegether, in EXACTLY the same way. In fact, we can transform the problem in a very simple way, by replacing (x+y) with z.

Now your problem reduces to:

syms z
eq1 = -sin(z)+cos(z-1.6)== 0
eq2 = cos(z)+cos(z-3.2)== 0

There is no more and no less information content in the problem. Surely you can agree, since x+y ALWAYS appear in exactly the same place, and always together.

solve(eq1,z)
ans =
pi/4 + 4/5
solve(eq2,z)
ans =
 -log(-exp(8i/5)*1i)*1i
  -log(exp(8i/5)*1i)*1i
  
vpa(ans)
ans =
 0.029203673205103380768678308360249
  -3.1123889803846898576939650749193

Solving eq1 for z, we find a simple solution. Solving eq2 for z, however, we get a completely different value for z. It is not really imaginary when we resolve it into a simpler numeric form. But see that it is not the first value we got for z.

So nothing in the universe will ever allow a solution to both equations for z, and therefore solving for x and y is just as impossible. It is very easy to write equations that have no solution. Surprise! You just did it.

MATLAB: Solving non linear equation using fsolve

You are not passing theta_n and other parameters to root2d(). One fix is to make root2d a Nested Function. Also, you must choose a different initial point. phi0 = [10,10] worked for me.

function solve_it()
    beta_a = 10;
    alpha_n = 10 ;
    eta= 18;
    i = 18;
    theta_i = 10;
    theta_n = 10 ;
    
    fun = @root2d;
    phi0 = [10,10];
    phi = fsolve(fun,phi0);
    phi_n = phi(1),
    phi_i = phi(2),
    function F = root2d(phi)
    F = zeros(2,1);
    F(1) = (pi*sin((pi*(phi(1) + theta_n))/180)*cos((pi*phi(2))/180)*(cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180)))/(180*sin((pi*phi(1))/180)*(cos((pi*(phi(1) + theta_n))/180)*cos((phi(2)*pi)/180) + sin((phi(2)*pi)/180)*tan((theta_i*pi)/180))^2) - (pi*cos((pi*phi(1))/180)*(cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180)))/(180*sin((phi(1)*pi)/180)^2*(cos((pi*(phi(1) + theta_n))/180)*cos((pi*phi(2))/180) + sin((pi*phi(2))/180)*tan((pi*theta_i)/180)));
    F(2) = ((cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180))*((pi*cos((pi*(phi(1) + theta_n))/180)*sin((pi*phi(2))/180))/180 - (pi*cos((pi*phi(2))/180)*tan((pi*theta_i)/180))/180))/(sin((pi*phi(1))/180)*(cos((pi*(phi(1) + theta_n))/180)*cos((phi(2)*pi)/180) + sin((phi(2)*pi)/180)*tan((theta_i*pi)/180))^2);
    end
end

Best Answer

Related Solutions

MATLAB: Solving symbolic trig equation

MATLAB: Solving non linear equation using fsolve

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