These solutions may be easily understood by noting that all of the terms on the right-hand sides of the original differential equations are proportional to formula_3. The equations may thus be divided through by formula_3, and the time rescaled so that the differential operator on the left-hand side becomes simply formula_48, where formula_49, i.e. formula_50. The differential equations are now all linear, and the third equation, of the form formula_51 const., shows that formula_52 and formula_4 (and formula_54 above) are simply linearly related.