a) Solving the initial value problem (I.V.P.) y' : passes through the point (xo, yo) with O xo = 2, yo = 0 Oxo = 0, yo = 2 xo = 0, yo = 0, = xy/(x - 1), y(0) = 2 implies finding a solution y(x) of the differential equation that b) The solution(s) of the I. V. P. in point (a) is/are OI OI and II O III where I:y(x) = 2e*(1 − x), II:y(x) = 2x(x − 1), III:y(x) = 2x(x − 1) + C. c) Consider the rectangular region D around the point (xo, yo) of width 2A along the x coordinate and height 2B along the y coordinate. The condition(s) that guarantee the existence and uniqueness of the solution to the IVP in a) are OI and II OII O II and III OIV OV OI and V 1:0 < A < 1 II:A ≤ (1-A)B A(B+2) III:0 < B < 2 IV:A ≤ (A+1)B A(2-B) V:A ≤ (A+1)B A(B+2)
a) Solving the initial value problem (I.V.P.) y' : passes through the point (xo, yo) with O xo = 2, yo = 0 Oxo = 0, yo = 2 xo = 0, yo = 0, = xy/(x - 1), y(0) = 2 implies finding a solution y(x) of the differential equation that b) The solution(s) of the I. V. P. in point (a) is/are OI OI and II O III where I:y(x) = 2e*(1 − x), II:y(x) = 2x(x − 1), III:y(x) = 2x(x − 1) + C. c) Consider the rectangular region D around the point (xo, yo) of width 2A along the x coordinate and height 2B along the y coordinate. The condition(s) that guarantee the existence and uniqueness of the solution to the IVP in a) are OI and II OII O II and III OIV OV OI and V 1:0 < A < 1 II:A ≤ (1-A)B A(B+2) III:0 < B < 2 IV:A ≤ (A+1)B A(2-B) V:A ≤ (A+1)B A(B+2)
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:a) Solving the initial value problem (I.V.P.) y' = xy/(x - 1), y(0) = 2 implies finding a solution y(x) of the differential equation that
passes through the point (xo, yo) with
x0 =
2, yo = 0 xo =
0, yo
=
2 xo = 0, yo = 0,
Ο
b) The solution(s) of the I. V. P. in point (a) is/are
OI OI and II O III
-
where I:y(x) = 2e*(1 − x), II:y(x) = 2x(x − 1), III:y(x) = 2x(x − 1) + C.
c) Consider the rectangular region D around the point (xo, yo) of width 2A along the x coordinate and height 2B along the y coordinate.
The condition(s) that guarantee the existence and uniqueness of the solution to the IVP in a) are
OI and II OIIO II and III OIV OV OI and V
1:0 < A < 1 II: A ≤
(1-A)B
A(B+2)
III:0 < B < 2 IV:A <
(A+1) B
A(2-B)
V:A ≤
(A+1)B
A(B+2)
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