Consider a function g € C¹([-1, 1] x R¹, Rª), and let y=C¹([1,1],Rd) be a solution of the initial value problem y'(x) = sin(g(x, y(x))) Vx (-1, 1), y(-1) = 1. What is the largest pen for which we definitely have yeCP([-1,1],Rº)? (Hint: Make a guess for p based on theorems from the lecture. When constructing a counterexample for p+1, keep it simple. Use a scalar function g that does not depend on y, and that is C¹, but not C².) O a. The initial value problem does not possess any solution. O b. p=0 O c. p=1 O d. p=2 O e. p=3 O f. p=4 O g. p=5 Oh. p=0o, or, in other words, we definitely have yeC([-1,1], Rd)
Consider a function g € C¹([-1, 1] x R¹, Rª), and let y=C¹([1,1],Rd) be a solution of the initial value problem y'(x) = sin(g(x, y(x))) Vx (-1, 1), y(-1) = 1. What is the largest pen for which we definitely have yeCP([-1,1],Rº)? (Hint: Make a guess for p based on theorems from the lecture. When constructing a counterexample for p+1, keep it simple. Use a scalar function g that does not depend on y, and that is C¹, but not C².) O a. The initial value problem does not possess any solution. O b. p=0 O c. p=1 O d. p=2 O e. p=3 O f. p=4 O g. p=5 Oh. p=0o, or, in other words, we definitely have yeC([-1,1], Rd)
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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![Consider a function
and let y=C¹([-1,1],Rd) be a solution of the initial value problem
g € C¹([-1, 1] × Rª, Rª),
y'(x) = sin(g(x, y(x))) \x=(−1, 1),
What is the largest pen for which we definitely have y=CP([-1,1],Rd)?
(Hint: Make a guess for p based on theorems from the lecture. When constructing a counterexample for p+1, keep it simple. Use a scalar function g
that does not depend on y, and that is C¹, but not C².)
O a. The initial value problem does not possess any solution.
O b. p=0
O c. p=1
d. p=2
p=3
O f. p=4
g. p=5
Oh. p=∞, or, in other words, we definitely have yeC([-1,1],Rd)
O
O e.
y(-1) = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fe1fc35-672a-49fd-831b-9642c77888ed%2F8c76e4f6-d2d7-4f52-b210-9c239e4fc2d9%2Fh4as4rm_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a function
and let y=C¹([-1,1],Rd) be a solution of the initial value problem
g € C¹([-1, 1] × Rª, Rª),
y'(x) = sin(g(x, y(x))) \x=(−1, 1),
What is the largest pen for which we definitely have y=CP([-1,1],Rd)?
(Hint: Make a guess for p based on theorems from the lecture. When constructing a counterexample for p+1, keep it simple. Use a scalar function g
that does not depend on y, and that is C¹, but not C².)
O a. The initial value problem does not possess any solution.
O b. p=0
O c. p=1
d. p=2
p=3
O f. p=4
g. p=5
Oh. p=∞, or, in other words, we definitely have yeC([-1,1],Rd)
O
O e.
y(-1) = 1.
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