Mathematics 9709 · AS & A Level · Differential equations

Differential equations — practice question

In one country, the government levies tax on every litre of petrol sold to motorists. The yearly revenue, in $R$ million dollars, depends on the tax rate $x$ dollars per litre. The relationship between $R$ and $x$ is represented by the differential equation $\frac{dR}{dx} = R\left(\frac{1}{x} - 0.57\right)$, with $R$ and $x$ treated as continuous variables. When $x = 0.5$, $R = 16.8$.
(i)[6]

Solve the differential equation to obtain $R$ as a function of $x$.

(ii)[3]

This model shows that $R$ has an upper limit. Find this maximum value of $R$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Separate the variables correctly and try integrating at least one side

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