State a region in the x-y-plane, where the hypotheses of Picard's theorem (namely: continuity of f(x, y) and Of(x, y)/ay) are satisfied and that contains the initial point (ro, yo). Thus, Picard's theorem allows you to conclude that there exists a unique solution through each given initial point in this region. y(0) = 1 (b) y'= (1-x² - y²) ¹/2, y(0) = 0 (c) y'=3(x+y)-2, y(0) = -1 (a) y' - x-y 2x + 5y
State a region in the x-y-plane, where the hypotheses of Picard's theorem (namely: continuity of f(x, y) and Of(x, y)/ay) are satisfied and that contains the initial point (ro, yo). Thus, Picard's theorem allows you to conclude that there exists a unique solution through each given initial point in this region. y(0) = 1 (b) y'= (1-x² - y²) ¹/2, y(0) = 0 (c) y'=3(x+y)-2, y(0) = -1 (a) y' - x-y 2x + 5y
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
Needed to be solved A,B and C correctly in 30 minutes
Please don't copy from Chegg
So the workflow for Part 1 is basically.
1. Determine if there's any undefined areas in the ODE
2. State a rectangle where the ivp exists, but the rectangle doesn't cover any undefined areas.
3.Then you differentiate f(x,y) partially with respect to y
4.and if the function is not continuous where the IVP is then there isn't a solution and if the partial derivative isn't continuous where the IVP is then there isn't a unique solution... you have to state that
Transcribed Image Text:State a region in the x-y-plane, where the hypotheses of Picard's theorem (namely: continuity of f(x, y)
and Of(x, y)/ay) are satisfied and that contains the initial point (ro, yo). Thus, Picard's theorem allows
you to conclude that there exists a unique solution through each given initial point in this region.
x-y
y(0) = 1
2x + 5y
(b) y'= (1-x² - y²) ¹/2, y(0) = 0
(c) y'= 3(x+y)-2,
y(0) = -1
In|ry|
y(1) = 2
1-x² + y²¹
1+x²
3y - y²¹
(cot (x))y
1+y
(a) y'
(d) y'
(e)
(f)
-
=
dy
dr
dy
dx
=
=
y(0) = 1
y(π/2) = 0
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