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. 9. y'=(1-2x) y², y(0) = -1/6
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. 9. y'=(1-2x) y², y(0) = -1/6
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.6: Wind And Water Current Problems
Problem 14OE
Related questions
Question
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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.
9.
y'=(1-2x) y², y(0) = -1/6
10.
y'=(1-2x)/y, y(1) = -2
11. xdx+ye dy = 0, y(0) = 1
dr/d0 = r²/0, r(1) = 2
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' =
1+3x²
3y² - 6y
y(0) = 1
and determine the interval in which the solution is valid.
integral curve has a vertical tangent.
Hint: To find the interval of definition, look for points where the
G 18. Solve the initial value problem
y' =
3.x²
3y²-4' (1) = 0
and determine the interval in which the solution is valid.
Hint: To find the interval of definition, look for points whe
integral curve has a vertical tangent.
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Given that a initial problem and we find its solution and plot the graph of this problem solution.
y' = (1-2x)y2 ; y(0)= -1/6
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