Let the population of living fish at time t (years) be denoted by x(t) (tonnes). An initial quantity of x0 tonnes of fish will be put into the lake at time t = 0. The net rate of change of the fish population in tonnes of fish per year is dx - = 0.5x = x² - f, x(0) = = x0 dt where xo) and f are non-negative constants and f represents the fish-harvesting rate. (a) Taking f = 0, write down the resulting differential equation stating clearly the solution method used.

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