Solving the initial value problem (IVP) y' = y/(x ln x), y(e) =1 implies finding a solution y(x) of the differential equation that passes rough the point (xo, Yo) with %3D Dro = 1, yo = e Ozo = e, yo = 1 Oro = 2.7, yo = 1 If this IVP has a unique solution, it means that there exists a rectangular region of the two dimensional ry plane whose center is the point (xo, yo) where the solution to the IVP is unique. in the whole ry plane, there exist one and only one solution passing through this point. there is only one unique solution to the ODE in the ry plane. The solution(s) of the I. V. P. in point (a) is/are Ol OlI Ol and II Ol and III Oll and III oro I'al m ) a ln - In III-ad) – (In ln le
Solving the initial value problem (IVP) y' = y/(x ln x), y(e) =1 implies finding a solution y(x) of the differential equation that passes rough the point (xo, Yo) with %3D Dro = 1, yo = e Ozo = e, yo = 1 Oro = 2.7, yo = 1 If this IVP has a unique solution, it means that there exists a rectangular region of the two dimensional ry plane whose center is the point (xo, yo) where the solution to the IVP is unique. in the whole ry plane, there exist one and only one solution passing through this point. there is only one unique solution to the ODE in the ry plane. The solution(s) of the I. V. P. in point (a) is/are Ol OlI Ol and II Ol and III Oll and III oro I'al m ) a ln - In III-ad) – (In ln le
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 (IVP) y' = y/(x ln x), y(e) = 1 implies finding a solution y(x) of the differential equation that passes
through the point (xo, Yo) with
Oxo = 1, yo = e
Oxo = e, yo =1
Oxo = 2.7, yo = 1
b) If this IVP has a unique solution, it means that
Othere exists a rectangular region of the two dimensional ry plane whose center is the point (xo, Yo) where the solution to the IVP is unique.
Oin the whole æy plane, there exist one and only one solution passing through this point.
Othere is only one unique solution to the ODE in the xy plane.
c) The solution(s) of the I. V. P. in point (a) is/are
OI
Ol
OlI
Ol and II
Ol and III
Oll and II
where I:y(x) = e ln æ, II:y(x) = ln æ, III:y(x) = (In ln æ)/e.
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