I think you're solution is 0 everywhere.

In[23]:= r = -3;
eqn = x'[t] == r*x[t] + 4*x[t]^3;
sol = DSolve[{eqn, x[0] == 0}, x, {t, 0, 100}]

During evaluation of In[23]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>

During evaluation of In[23]:= Solve::ifun: Inverse functions are being used by Solve, so some solutions may not be found; use Reduce for complete solution information. >>

Out[25]= {{x -> Function[{t}, 0]}}