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d) x²y' - 4xy = x sin(x), x>0 e) y' - 2y = f(x), y(0) = 1, where f(x) = y(0) = 1, where ƒ(x) = { f) sin(x)y' + y cos(x) = sin(2x), y(π/2) = 3 1x, 0, if x < 1 if x ≥ 1

d) x²y' - 4xy = x sin(x), x>0 e) y' - 2y = f(x), y(0) = 1, where f(x) = y(0) = 1, where ƒ(x) = { f) sin(x)y' + y cos(x) = sin(2x), y(π/2) = 3 1x, 0, if x < 1 if x ≥ 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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I only need help with parts d, e, and f. Thank you. Please show all steps clearly. 

Solve the following (first order & linear!) differential equations: a) + 2y(x) = 2e-x b) d=122y(x) + (1+²²)² (1+x2)2 c) + ay(x) = b sin(wx) d) x²y' - 4xy = x sin(x), (a, b, w are constants.) x>0 1- x, e) y′ – 2y = f(x), _y(0) = 1, where ƒ(a) = { } 0, f) sin(x)y' + y cos(x) = sin(2x), y(T/2) = 3 if x < 1 if x ≥ 1
Transcribed Image Text:Solve the following (first order & linear!) differential equations: a) + 2y(x) = 2e-x b) d=122y(x) + (1+²²)² (1+x2)2 c) + ay(x) = b sin(wx) d) x²y' - 4xy = x sin(x), (a, b, w are constants.) x>0 1- x, e) y′ – 2y = f(x), _y(0) = 1, where ƒ(a) = { } 0, f) sin(x)y' + y cos(x) = sin(2x), y(T/2) = 3 if x < 1 if x ≥ 1
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