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(d) x²y" — 7xy' + 16y = 0, - ..!! 16a Y₁ = x¹; (102)

(d) x²y" — 7xy' + 16y = 0, - ..!! 16a Y₁ = x¹; (102)

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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(d) and (e) please.

My solution for (d) is y2(x) = x^4 ln(x) and for (e)(-cos(4x))/4 but I feel like something is not correct...

4. Given the solution y₁(x) to the five homogeneous linear ODEs listed below, use reduction of order to find a second solution to these ODES: e2x (a) y" — 4y' + 4y = 0, (b) (1 – 2x − x²)y" + 2(1+x)y' – 2y = 0, (c) xy"+y' = 0 Y₁ = ln x; (d) x²y" — 7xy' + 16y = 0, (e) y" + 16y=0, Y₁ = sin(4x). у1 (Straightforward; perhaps a little tedious.) Y1 = Y₁ = x¹; Y₁ = x + 1
Transcribed Image Text:4. Given the solution y₁(x) to the five homogeneous linear ODEs listed below, use reduction of order to find a second solution to these ODES: e2x (a) y" — 4y' + 4y = 0, (b) (1 – 2x − x²)y" + 2(1+x)y' – 2y = 0, (c) xy"+y' = 0 Y₁ = ln x; (d) x²y" — 7xy' + 16y = 0, (e) y" + 16y=0, Y₁ = sin(4x). у1 (Straightforward; perhaps a little tedious.) Y1 = Y₁ = x¹; Y₁ = x + 1
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