checkErrorBetweenSolutions.m

% Define symbolic variables
syms a1 a2 a3 a4 C1 C2 C3 C4 k x

% phiSol1 in exponential form
phiSol1 = a1 * exp(-x * k) + a2 * exp(x * k) + ...
          a3 * exp(-x * k * 1i) + a4 * exp(x * k * 1i);

% phiSol2 in trigonometric and hyperbolic form
phiSol2 = C1 * sin(k * x) + C2 * cos(k * x) + ...
          C3 * sinh(k * x) + C4 * cosh(k * x);

% Transform phiSol1 into trigonometric and hyperbolic forms using Euler's formula
phiSol1_transformed = simplify(expand(phiSol1));

% Display the transformed phiSol1 and original phiSol2 for visual comparison
disp('Transformed phiSol1:');
disp(phiSol1_transformed);
disp('Original phiSol2:');
disp(phiSol2);

% Assuming structural equivalence, set up equations to find the relationship between coefficients
coeffs_eqns = [a1 + a2 == C4, a1 - a2 == C3, a3 + a4 == C2, 1i*(a4 - a3) == C1];

% Solve the equations for the coefficients
coeffs_solutions = solve(coeffs_eqns, [a1, a2, a3, a4]);

% Display the relationships between the coefficients
disp('Relationships between coefficients:');
disp(coeffs_solutions);