vpasolve: Cannot differentiate the equation

Hello friends,

I need to solve some nonlinear equation defined symbolically, using vpasolve.Specifically arc length parameterization of a curve y=u^2-u^3. I need to find the value of u for a given arc length of the curve. I am getting an error. If I change the curve equation to y=u^2-u, the code works fine. It seems there is a problem with the integral. Someone kindly help me to troubleshoot this issue. Is there any other ways I can solve a symbolic equation numerically.

clear; clc
syms u
y=u^2-u^3; % Curve equation
%y=u^2-u; % This curve is giving solution!!
arc_length=1;% prescribed arc length of the curve
objective_function=int(sqrt(1+(diff(y))^2),u); % Arc length of the curve from u=0 to u=u
f1=subs(objective_function,u); % Definite integral upper limit evaluation
f2=subs(objective_function,0); %Definite integral lower limit evaluation
vpasolve(f1-f2==arc_length,u)

Error:
Error using mupadengine/feval (line 166)
Cannot differentiate the equation.

Error in sym/vpasolve (line 172)
    sol = eng.feval('symobj::vpasolve',eqns,vars,X0);

Error in vpa_solver_issue (line 7)
vpasolve(f1-f2==arc_length,u)

[darova]

What about numerical solution?

[Sreejath S]

Yes, Numerical solution worked for this case. Thanks!!