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Here's the solution, the mistake was with brackets [mcode] w = NDSolve[{D[u[r, thet, t], t] == D[u[r, thet, t], {r, 2}] + (1/r) D[u[r, thet, t], r] + (1/r^2) D[ u[r, thet, t], {thet, 2}] + u[r, thet, t] (1 - u[r, thet, t] - c*x[r,...