Using the ideas of supersymmetric quantum mechanics, we exactly solve a continuous family of anharmonicrnpotentials, which are the supersymmetric partners of the linear harmonic oscillators. The family includes a series ofrnpotentials in which the excited-state energy is the same as that of the harmonic oscillators, but the ground-state energyrncan be any value lower than the excited states. The shape of the potential is variable, which includes the double-wellrnand triple-well potentials. All the potentials obtained in this paper are free of singularities, and the supersymmetry ofrnthe solutions is unbroken.
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