Chapter 2.1: First Order Linear Equations

Question 1

Standard Form of a First Order Linear Equation

Answer 1

u’+p(t)u=q(t)

Question 2

homogeneous equation

Answer 2

u’+p(t)u=0

Question 3

Is the homogeneous equation separable?

Answer 3

Yes

Question 4

Source or forcing term

Answer 4

q(t)

Question 5

Integrating factors

Answer 5

e^P(t)

Question 6

Theorem 2.4

Answer 6

The general solution is the sum of the general solution to the homogeneous equation plus any solution to the nonhomogeneous equation.

Question 7

Newton’s Law of Cooling

Answer 7

T’+hT=hT_(e) (t)

Question 8

RC Circuit

Answer 8

First order, linear, standard form

Question 9

Chemical Reactor

Answer 9

First order, linear, must be changed to standard form

Question 10

Sales Response to Advertising

Answer 10

S’=-(a+(rA(t))/M)S+rA(t)