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Q16 E

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Found in: Page 5

Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069

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.

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.

See the step by step solution

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.