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Consider the differential equation xy" + (3x − 1)y' – 3y = 0 (x > 0). -3x (a) Verify that y₁(x) = e is a solution to this equation. (b) Use the method of reduction of order to find the general solution to this differential equation. Hint: You may find the following integral useful [re²² dz-²¹-re²²-² 1 ax xe dọc ax a ૨૨૯ (c) Hence find the particular solution for y(1) = 2 + e¯³, y'(0) = 0. = ax

Consider the differential equation xy" + (3x − 1)y' – 3y = 0 (x > 0). -3x (a) Verify that y₁(x) = e is a solution to this equation. (b) Use the method of reduction of order to find the general solution to this differential equation. Hint: You may find the following integral useful [re²² dz-²¹-re²²-² 1 ax xe dọc ax a ૨૨૯ (c) Hence find the particular solution for y(1) = 2 + e¯³, y'(0) = 0. = ax

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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Consider the differential equation xy" + (3x − 1)y' – 3y = 0 (x > 0). -3x (a) Verify that y₁(x) = e is a solution to this equation. (b) Use the method of reduction of order to find the general solution to this differential equation. Hint: You may find the following integral useful [re²² dz-²¹-re²²-² 1 ax xe dọc ax a ૨૨૯ (c) Hence find the particular solution for y(1) = 2 + e¯³, y'(0) = 0. = ax
Transcribed Image Text:Consider the differential equation xy" + (3x − 1)y' – 3y = 0 (x > 0). -3x (a) Verify that y₁(x) = e is a solution to this equation. (b) Use the method of reduction of order to find the general solution to this differential equation. Hint: You may find the following integral useful [re²² dz-²¹-re²²-² 1 ax xe dọc ax a ૨૨૯ (c) Hence find the particular solution for y(1) = 2 + e¯³, y'(0) = 0. = ax
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