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a) c) ry" + 3y = x, y(1) = 1, y' (1) = 2. x(x-4)y' + 3xy + 4y = 2, y (3) = 0, y (3) = -1. b) d) (x-1)y"-3xy' + 4y = sinx, y(-2) = 2, y'(-2) = 1. y" + (cos x)y' + 3(ln |x|)y = 0, y (2) = 3, y/(2) = 1

a) c) ry" + 3y = x, y(1) = 1, y' (1) = 2. x(x-4)y' + 3xy + 4y = 2, y (3) = 0, y (3) = -1. b) d) (x-1)y"-3xy' + 4y = sinx, y(-2) = 2, y'(-2) = 1. y" + (cos x)y' + 3(ln |x|)y = 0, y (2) = 3, y/(2) = 1

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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Problem 10.1. In each of the following problems determine the longest interval in which the given initial value problem is certain to have a unique solution. Do not attempt to find the solution. a) c) G ry" + 3y = x, y (1) = 1, y (1) = 2. x(x-4)y' + 3xy' + 4y = 2, y (3) = 0, y (3) = -1. x³y" - x²y" + xy + 3y = 0, y(1) = 0, y'(1) = 1, y" (1) = 2. b) a (x-1)y"-3xy + 4y = sinx, y (-2) = 2, y'(-2) = 1. y" + (cos x)y' + 3(lnx) y = 0, y (2) = 3, y'(2) = 1 (x-1)y" - xy" + 3y = cos 2x, y (0) = -1, y'(0) = 1, y" (0) = 2.
Transcribed Image Text:Problem 10.1. In each of the following problems determine the longest interval in which the given initial value problem is certain to have a unique solution. Do not attempt to find the solution. a) c) G ry" + 3y = x, y (1) = 1, y (1) = 2. x(x-4)y' + 3xy' + 4y = 2, y (3) = 0, y (3) = -1. x³y" - x²y" + xy + 3y = 0, y(1) = 0, y'(1) = 1, y" (1) = 2. b) a (x-1)y"-3xy + 4y = sinx, y (-2) = 2, y'(-2) = 1. y" + (cos x)y' + 3(lnx) y = 0, y (2) = 3, y'(2) = 1 (x-1)y" - xy" + 3y = cos 2x, y (0) = -1, y'(0) = 1, y" (0) = 2.
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