1. Solve each of the following initial value problems and plot the solutions for several values of yo. Then describe in a few words how the solutions resemble, and differ from, each other. a. dy/dt = -y +5, b. dy/dt = -2y +5, c. dy/dt = -2y + 10, y(0) = yo y(0) = yo y(0) = yo
1. Solve each of the following initial value problems and plot the solutions for several values of yo. Then describe in a few words how the solutions resemble, and differ from, each other. a. dy/dt = -y +5, b. dy/dt = -2y +5, c. dy/dt = -2y + 10, y(0) = yo y(0) = yo y(0) = yo
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
1 pleas
Transcribed Image Text:Problems
N 1. Solve each of the following initial value problems and plot
the solutions for several values of yo. Then describe in a few words
how the solutions resemble, and differ from, each other.
y(0) = yo
y(0) = yo
a. dy/dt = -y +5,
b. dy/dt = -2y + 5,
c. dy/dt = -2y + 10,
2. Follow the instructions for Problem 1 for the following
initial-value problems:
a. dy/dt = y = 5, y(0) = yo
-
G b. dy/dt = 2y = 5,
c. dy/dt = 2y - 10,
3. Consider the differential equation
G
y(0) = yo
y(0) = yo
-
y(0) = yo
dy/dt = = -ay+b,
where both a and b are positive numbers.
a. Find the general solution of the differential equation.
Gb. Sketch the solution for several different initial conditions.
c. Describe how the solutions change under each of the
following conditions:
i. a increases.
ii. b increases.
III. Both a and b increase, but the ratio b/a remains the same.
4. Consider the differential equation dy/dt = ay-b.
a. Find the equilibrium solution ye.
=
y Ye; thus Y(t) is the deviation from the
b. Let Y(1)
equilibrium solution. Find the differential equation satisfied by
Y(1).
N
сс
ca
m
0
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