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Chapter 1: Q15 E (page 5)

In Problems 13-16, write a differential equation that fits the physical description. The rate of change in the temperature T of coffee at time t is proportional to the difference between the temperature M of the air at time t and the temperature of the coffee at time t.

Short Answer

Expert verified

dTdt=kM-Twhere k is the constant of proportionality.

Step by step solution

01

Analyzing the given statement

By analyzing the given statement,

dTdt∝M-T, where T is the temperature of coffee at time t and M is the air temperature at time t.

02

Writing the differential equation

dTdt=kM-T, where k is the constant of proportionality.

Hence, dTdt=kM-T is the required differential equation.

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Most popular questions from this chapter

Decide whether the statement made is True or False. The function y(x)=-13(x+1) is a solution to dydx=y-1x+3.

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

(b) Show thatxy3-xy3sinx=1 is an implicit solution todydx=xcosx+sinx-1y3x-xsinx on the interval (0,π2).

In Problems 9–20, determine whether the equation is exact.

If it is, then solve it.

(2xy+3)dx+(x2-1)dy=0

In Problems 23-28, determine whether Theorem 1 implies that the given initial value problem has a unique solution.

dydx=3x-y-13,y(2)=1

In problems 1-4 Use Euler’s method to approximate the solution to the given initial value problem at the points x=0.1,0.2,0.3,0.4, and 0.5, using steps of size 0.1h=0.1.

dydx=-xy,y(0)=4
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