y' = xy³ (1+x²)-1/2, y(0) = 1
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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Transcribed Image Text:form.
on of the given initial value problem in explicit
b. Plot the graph of the solution.
solution is defined.
c. Determine (at least approximately) the interval in which the
y'=(1-2x) y²,
y(0) = -1/6
y'=(1-2x)/y, y(1) = -2
xdx+ye*dy = 0, y(0) = 1
9.
10.
11.
12. dr/d0 = r²/0, r(1) = 2
13. y'=xy³ (1+x²)-1/2, y(0) = 1
14. y' = 2x/(1+2y), y(2) = 0
15. 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'
y' =
1+3x²
3y² - 6y
and determine the interval in which the solution is valid.
Hint: To find the interval of definition, look for points where the
integral curve has a vertical tangent.
G 18. Solve the initial value problem
=
y(0) = 1
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 where the
integral curve has a vertical tangent.
2.
w
24
wh
beh
Ho
dy
onl
can
the
hom
The
conte
the he
Transcribed Image Text:form.
on of the given initial value problem in explicit
b. Plot the graph of the solution.
solution is defined.
c. Determine (at least approximately) the interval in which the
y'=(1-2x) y²,
y(0) = -1/6
y'=(1-2x)/y, y(1) = -2
xdx+ye*dy = 0, y(0) = 1
9.
10.
11.
12. dr/d0 = r²/0, r(1) = 2
13. y'=xy³ (1+x²)-1/2, y(0) = 1
14. y' = 2x/(1+2y), y(2) = 0
15. 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'
y' =
1+3x²
3y² - 6y
and determine the interval in which the solution is valid.
Hint: To find the interval of definition, look for points where the
integral curve has a vertical tangent.
G 18. Solve the initial value problem
=
y(0) = 1
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 where the
integral curve has a vertical tangent.
2.
w
24
wh
beh
Ho
dy
onl
can
the
hom
The
conte
the he
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