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Chapter 1: Q16 E (page 5)

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.

Short Answer

Expert verified

The differential equation suitable for the given condition is dAdt=A2, where A is the mass of salt at a time t.

Step by step solution

01

Analysing the given statement

By analyzing the given statement,

dAdt鈭�A2, where A is the mass of salt at a time t.

02

Writing the differential equation

dAdt=kA2, where k is the constant of proportionality.

Hence, dAdt=kA2 is the required differential equation.

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Most popular questions from this chapter

In problems 1-6, identify the independent variable, dependent variable, and determine whether the equation is linear or nonlinear.

t3d3xdt32+3t-x=0

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(a)y(0)=2,y'(0)=1

(b)y(1)=1,y'(1)=0

(a) Show that y2+x-3=0 is an implicit solution todydx=-12y on the interval (-鈭�,3).

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