In each of Problems 13 through 16, draw a direction field and plot (or sketch) several solutions of the given differential equation. Describe how solutions appear to behave as t increases and how their behavior depends on the initial value yo when t = 0. G 13. y'= ty(3 - y)
In each of Problems 13 through 16, draw a direction field and plot (or sketch) several solutions of the given differential equation. Describe how solutions appear to behave as t increases and how their behavior depends on the initial value yo when t = 0. G 13. y'= ty(3 - y)
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
13
Transcribed Image Text:defining solutions
ularities of solutions of nonlinear equations
and examining the solution. It is likely that
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In each of Problems 13 through 16, draw a direction field and plot (or
sketch) several solutions of the given differential equation. Describe
how solutions appear to behave as t increases and how their behavior
depends on the initial value yo when t = 0.
G 13. y'= ty(3-y)
y'= y(3-ty)
G 14.
G 15. y'=-y(3- ty)
G 16. y'=t-1-y²
17. Consider the initial value problem y' = y¹/3, y(0) = 0 from
Example 3 in the text.
a. Is there a solution that passes through the point (1, 1)? If so,
find it.
b. Is there a solution that passes through the point (2, 1)? If so,
find it.
c. Consider all possible solutions of the given initial value
problem. Determine the set of values that these solutions have
at t = 2.
18. a. Verify that both y₁ (t) = 1- t and y₂(t) = -t²/4 are
solutions of the initial value problem
-1+√² +4y
2
Where are these solutions valid?
=
"
y(2) = -1.
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