Math 2250-1
Workout Wednesday Week 3
Name and Unid:
1. (10 points) Solve the DE:
1
dx
= 2
dt
t
With x(1) = 1. If x(t) is a distance, how far does x travel as t → ∞
Solution: This is solved by direct integration
Z
Z
1
dx =
dt + C
t2
1
x(t) = − + C
t
1 = −1 + C =⇒ C = 2
2. (10 points) Solve the DE:
dx
x
= + te−t
dt
t
With x(1) = 3.
(1)
(2)
(3)
Solution: This is linear first order:
ρ = e−
R
1
dt
t
(4)
1
t
(5)
ρQ = e−t
(6)
ρ = e− ln(t) =
d
[ρx] = e−t
dt
x
= −e−t + C
t
x(t) = Ct − te−t
C=4
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(7)
(8)
(9)
(10)
3. (10 points) Identify the equilibrium points x∗ and stability of the following DE. Then
solve the DE with x(0) = 0:
dx
= x2 − 4x + 3
dt
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