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) G 14. y'= y(3-ty) G 15. y'=-y(3-ty) G 16. y'=1-1-y²
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) G 14. y'= y(3-ty) G 15. y'=-y(3-ty) G 16. y'=1-1-y²
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:9:45
an equation defining solutions
olutions of nonlinear equations
ing the solution. It is likely that
on the differential equation.
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.
13. y'=ty(3-y)
G 14. y'= y(3- ty)
G 15. y'=-y(3-ty)
G 16. y'=1-1-y²
854
17. Consider the initial value problem y' =
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.
X
B. a. Verify that both y₁ (t) = 1 - t and y₂(1)
solutions of the initial value problem
y' =
-1+√√²+4y
2
Where are these solutions valid?
yl/3, y(0) = 0 from
c. Consider all possible solutions of the given initial value
problem. Determine the set of values that these solutions have
at t = 2.
-1²/4 are
y (2) = -1.
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