Answered: (d) y' = dy dr (e) In ry 1-x² + y²¹ -…

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(d) y' = dy dr (e) In ry 1-x² + y²¹ - dy (f) = dr 1+x² 3y - y²¹ (cot(x))y 1+y y(1) = 2 y(0) = 1 y(π/2) = 0

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.5: Applications

Problem 2EQ

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Question

Needed to be solved D,E and F 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

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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