9 the question and the final answer
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
9
the question and the final answer
Transcribed Image Text:dx
y
In each of Problems 9 through 16:
a. Find the solution of the given initial value problem in explicit
form.
Gb. Plot the graph of the solution.
c. Determine (at least approximately) the interval in which the
solution is defined.
14.
15.
9.
y(0) = -1/6
10.
y(1) = -2
11. xdx+ye dy = 0, y(0) = 1
12.
dr/d0 = r²/0, r(1) = 2
13.
y'=xy³(1+x²)-1/2, y(0) = 1
y' = 2x/(1+2y), y(2) = 0
y' = (3x² - e*)/(2y-5), y(0) = 1
16. sin(2x) dx + cos(3y) dy = 0, y(π/2) = π/3
Some of the results requested in Problems 17 through 22 can be
obtained either by solving the given equations analytically or by
plotting numerically generated approximations to the solutions. Try
to form an opinion about the advantages and disadvantages of each
approach.
G 17. Solve the initial value problem
y' = (1-2x) y²,
y'=(1-2x)/y,
y'
=
y(0) = 1
and determine the interval in which the solution is valid.
Hint: To find the interval of definition, look for points where the
1+ 3x²
3y² - 6y
integral curve has a vertical tangent.
G 18. Solve the initial value problem
y' =
3.x²
3y² - 4'
y(1) = 0
and determine the interval in which the solution is valid.
Hint: To find the interval of definition, look for points whe
23
wh
24.
whe
beh
Hor
dy/
only
can
the c
hom
The
conte
the he
Transcribed Image Text:dx
y
In each of Problems 9 through 16:
a. Find the solution of the given initial value problem in explicit
form.
Gb. Plot the graph of the solution.
c. Determine (at least approximately) the interval in which the
solution is defined.
14.
15.
9.
y(0) = -1/6
10.
y(1) = -2
11. xdx+ye dy = 0, y(0) = 1
12.
dr/d0 = r²/0, r(1) = 2
13.
y'=xy³(1+x²)-1/2, y(0) = 1
y' = 2x/(1+2y), y(2) = 0
y' = (3x² - e*)/(2y-5), y(0) = 1
16. sin(2x) dx + cos(3y) dy = 0, y(π/2) = π/3
Some of the results requested in Problems 17 through 22 can be
obtained either by solving the given equations analytically or by
plotting numerically generated approximations to the solutions. Try
to form an opinion about the advantages and disadvantages of each
approach.
G 17. Solve the initial value problem
y' = (1-2x) y²,
y'=(1-2x)/y,
y'
=
y(0) = 1
and determine the interval in which the solution is valid.
Hint: To find the interval of definition, look for points where the
1+ 3x²
3y² - 6y
integral curve has a vertical tangent.
G 18. Solve the initial value problem
y' =
3.x²
3y² - 4'
y(1) = 0
and determine the interval in which the solution is valid.
Hint: To find the interval of definition, look for points whe
23
wh
24.
whe
beh
Hor
dy/
only
can
the c
hom
The
conte
the he
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