Differential Equation Problem

April 8, 2026Mathematics

ScanSolve AI Answer

April 8, 2026

Answer

$\frac{dN}{dt} = \frac{k}{N}$

Here are the solutions to the problems.

12. Differential Equation Problem

a) (i) Form a differential equation for the rate of increase in the quantity of the commodity demanded. The rate of increase in quantity $N$ with respect to time $t$ is $\frac{dN}{dt}$ . It is inversely proportional to the quantity $N$ . $\frac{dN}{dt} \propto \frac{1}{N}$ Introducing a constant of proportionality $k$ : $\frac{dN{dt} = \frac{k}{N}}$

a) (ii) Solve the differential equation. Step 1: Separate the variables. $N \, dN = k \, dt$ Step 2

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Quick Answer

(dN)/(dt) = (k)/(N) a) (ii) Solve the differential equation. Step 1: Separate the variables.

Asked on April 8, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 8, 2026

Here are the solutions to the problems. 12. Differential Equation Problem a) (i) Form a differential equation for the rate of increase in the quantity of the commodity demanded. The rate of increase in quantity N with respect to time t is (dN)/(dt). It is inversely proportional to the quantity N. (dN)/(dt) (1)/(N) Introducing a constant of proportionality k: (dN)/(dt) = (k)/(N) a) (ii) Solve the differential equation. Step 1: Separate the variables. N \, dN = k \, dt Step 2