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solution is guaranteed. (b) = 2r²y²; y(1) = 1. = xln(y); y(1) = 1. =I 1; y(0) = 1. dy

solution is guaranteed. (b) = 2r²y²; y(1) = 1. = xln(y); y(1) = 1. =I 1; y(0) = 1. dy

Advanced Engineering Mathematics
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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(1) A more detailed version of Theorem I says that, if the function f(r,y) is continuous near the point (a, b), then at least one solution of the differential equation y'=f(r, y) exists on some open interval I containing the point z = a and, moreover, that if in addition the partial derivative of/oy is continuous near (a, b), then this solution is unique on some (perhaps smaller) interval J. Determine whether existence of at least one solution of the given initial value problem is thereby guaranteed and, if so, whether uniqueness of that solution is guaranteed. dy (a) = 2r²y²; (b) =ln(y); dy (c) y- =H 1; dr. dr y(1) = -1. y(1) = 1. y(0) = 1.
Transcribed Image Text:(1) A more detailed version of Theorem I says that, if the function f(r,y) is continuous near the point (a, b), then at least one solution of the differential equation y'=f(r, y) exists on some open interval I containing the point z = a and, moreover, that if in addition the partial derivative of/oy is continuous near (a, b), then this solution is unique on some (perhaps smaller) interval J. Determine whether existence of at least one solution of the given initial value problem is thereby guaranteed and, if so, whether uniqueness of that solution is guaranteed. dy (a) = 2r²y²; (b) =ln(y); dy (c) y- =H 1; dr. dr y(1) = -1. y(1) = 1. y(0) = 1.
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