On exact solutions for damped anharmonic oscillators

For arbitrary functions f1, f2 and f3 the anharmonic oscillator x+f1(t)x+f2(t)x+f3(t)x3=0 cannot be solved in closed form (i.e. the general solution cannot be expressed as elliptic functions). The authors apply the Painleve test to obtain the constraint on the functions f1, f2 and f3 for which the equation passes the test. The constraint on f1, f2 and f3 (i.e the differential equation which f1, f2, and f3 obey) is discussed and solutions are given.