I need to find the values of the constants

% Tanh–Coth Method for Solving Nonlinear ODEs
clear; clc; syms U(xi) a0 a1 a2 b1 b2 c xi

% Example ODE: U'' - U + 2*U^3 = 0
ode = U^2*diff(U, xi, 2)+diff(U,xi,1)*(2*U+1) + U^4+U^3;

% Step 1: Assume tanh–coth solution (up to order 2 for example)
U_trial = a0 + a1*tanh(xi) + a2*tanh(xi)^2 + b1*coth(xi) + b2*coth(xi)^2;

% Step 2: Substitute the trial function into the ODE
ode_sub = subs(ode, U, U_trial);

% Step 3: Expand and simplify
ode_simplified = simplify(expand(ode_sub));

% Step 4: Collect terms with respect to tanh and coth
% Convert to polynomial form in tanh(xi) and coth(xi)
ode_collected = collect(ode_simplified, [tanh(xi), coth(xi)]);

% Step 5: Equate coefficients of each power of tanh and coth to zero
% (To make the equation identically zero)
coeffs_tanh = coeffs(ode_collected, tanh(xi));
eqns = [];
for k = 1:length(coeffs_tanh)
    eqns = [eqns, simplify(coeffs_tanh(k)) == 0];
end

% Step 6: Solve for coefficients
sol = solve(eqns, [a0 a1 a2 b1 b2 d1 d2], 'IgnoreAnalyticConstraints', true);

disp('Solutions for coefficients:')
disp(sol)

[Alexander]

Hey i see different issues here:

• ode does not match the stated example. Make sure you’re solving the intended ODE.
• U_trial mixed tanh and coth without reducing identities → derivatives introduce sech^2/csch^2 and you never eliminated them.
• Try to prefer use one basis: e.g. tanh-only. If you keep coth, replace it with 1/tanh and multiply through by enough powers of tanh to clear denominators before collecting.
• Try to "simplify(ode)" and after that to substitute "subs(ode, sech(k*xi)^2, 1 - tanh(k*xi)^2)"
• solve(..., [a0 a1 a2 b1 b2 d1 d2]) referenced d1,d2 which you never declared?

[Walter Roberson]

Duplicated by later https://www.mathworks.com/matlabcentral/answers/2180534-please-help-me-to-solve-this-simple-error?s_tid=srchtitle