Math 2A
In-Class Activity Sections 2.2 (Separable), 3.2 (Modeling)
Names: _
A tank with perfect mixing initially contains 0.5kg salt dissolved in 100 L water. Salt water
with concentration 0.05 kg salt per liter flows in, at the rate of 8 L/min. The out-f
Math 2A
In-Class Activity
Sections 2.3 (Linear)
Names: _
A tank with perfect mixing initially contains 0.5kg salt dissolved in 100 L water. Salt water
with concentration 0.05 kg salt per liter flows in, at the rate of 8 L/min. The out-flow is also
10 L/mi
Math 2A
In-Class Activity
Sections 1.1, 3.1, 1.2
Names: _
1. Consider the differential equation
=
Which of the following is the general solution? Show how to verify.
i.
() = +
1
ii.
() = +
iii.
() = 2 +
2
1
2
2. A very simple but very important mathem
Consider 2 + = .
(A) Use the method of undetermined coefficients to find a particular solution to the differential equation.
(B) Use the method of variation of parameters to find a particular solution to the differential equation.
(C) Find the solution to
Math 2A
In-Class Activity
Sections 1.2, 1.3, phase line
Solid lines represent the x-axis and y-axis. Each tick mark is one unit.
1. Match each DE to its slope field, SF1 through SF10.
DE
Slope
Field
DE
=
=
=
=
2
=
=
= (4 )
4
=2
=
Slope
Field
= +
Math 2A
1.
In-Class Activity
( )
Sections 4.1, 4.2: Intro to CCLDEs
( )
a. Can the given IVP represent a spring-mass system? If so, describe the attributes of the
system and initial conditions. If not, describe how the system modeled by this IVP is
differ
Math 2A
In-Class Activity
Sections 4.2, 4.3:More CCLDEs
1. + + 4 = 0; (0) = 1; (0) = 0
a. Set up the quadratic formula to calculate the auxiliary equation roots.
b. Now plug in 3 different values for : = 2, = 4, and = 5.
In each case, find the general sol