Q16 E - Fundamentals Of Differential Equations And Boundary Value Problems

Question

In Problems 13-16, write a differential equation that fits the physical description. The rate of change of the mass A of salt at time t is proportional to the square of the mass of salt present at time t.

Step-by-Step Solution

Answer

The differential equation suitable for the given condition is $\frac{\mathrm{dA}}{\mathrm{dt}}={\mathrm{A}}^2$, where A is the mass of salt at a time t.

Step 1: Analysing the given statement

By analyzing the given statement,

$\frac{\mathrm{dA}}{\mathrm{dt}}\propto {\mathrm{A}}^2$, where A is the mass of salt at a time t.

Step 2: Writing the differential equation

$\frac{\mathrm{dA}}{\mathrm{dt}}={\mathrm{kA}}^2$, where k is the constant of proportionality.

Hence, $\frac{\mathbf{dA}}{\mathbf{dt}}\mathbf{=}{\mathbf{kA}}^{\mathbf{2}}$ is the required differential equation.