What is the general solution of the following differential equation? у?) + 5у 0) + 13у(5) + 17у(4) — 1Зу" - 33у - 65у + 75у (6) = 0 (1) у(x) — Сте* + Cэe — Зх +C3e +C4e¯* cos(2x)+c5e' -x sin(2x)+C6xe¯* cos(2x)+c7xe¯*sin(2x) -3x (2) y(x) = c1e3*+C2xe¯* cos(2x)+C3xe¯*sin(2x)+c4e* +cgxe* + C6e¯* cos(2x)+c7e¯*sin(2x) -3x (3) y(x) 3D С1 сos (2x) + C2 sin(2x) + Cҙe* + сAхе* + Cзе + C¢X Cos(2x) + c7x sin(2x) + c5x²e -3x -3x (4) y(x) = c1e* + c2xe* + c3e° + C4xe -3x + C6e° cos(2x) + c7e*sin(2x) -3x cos(2x) + C5xe¯*sin(2x) + C6x²e* cos(2x) + (5) у(х) C7x?e-* sin(2x) Cje* + C2e + C3xe¬3x + C4xe
What is the general solution of the following differential equation? у?) + 5у 0) + 13у(5) + 17у(4) — 1Зу" - 33у - 65у + 75у (6) = 0 (1) у(x) — Сте* + Cэe — Зх +C3e +C4e¯* cos(2x)+c5e' -x sin(2x)+C6xe¯* cos(2x)+c7xe¯*sin(2x) -3x (2) y(x) = c1e3*+C2xe¯* cos(2x)+C3xe¯*sin(2x)+c4e* +cgxe* + C6e¯* cos(2x)+c7e¯*sin(2x) -3x (3) y(x) 3D С1 сos (2x) + C2 sin(2x) + Cҙe* + сAхе* + Cзе + C¢X Cos(2x) + c7x sin(2x) + c5x²e -3x -3x (4) y(x) = c1e* + c2xe* + c3e° + C4xe -3x + C6e° cos(2x) + c7e*sin(2x) -3x cos(2x) + C5xe¯*sin(2x) + C6x²e* cos(2x) + (5) у(х) C7x?e-* sin(2x) Cje* + C2e + C3xe¬3x + C4xe
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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Transcribed Image Text:What is the general solution of the following differential equation?
//
+ 5y () + 13уб) + 17y(4) — 13у
>(5)
" — 33у
65у + 75у %3D 0
(9)*
-
-3x
(1) у(x) — С1е* + C2e
+ C3e
+C4e
+ сде * сos(2x) + cзе * sin(2х) + Cөхе * * sin(2x)
sin(2x) + C6хе
cos(2x) + с7хе
— Зх
(2) у(x) — сје
+ c2xe * сos(2х) + сҙхе *
X sin(2x) + сде* + Csxе* + Cве
Cos(2x) + с7e X sin(2x)
3x
(3) у(х)
— С1 сos (2x) + C2 sin(2x) + Сзе* + с4xе* + Cse
+ C6х сos(2x) + с7xsin(2xх)
¬3x
+ Cве Хсos(2х) + с7е X sin(2x)
3x
(4) у(x) — С1е* + c2xe* + cзе
3x
+ C4xe
+ C5x²e
+ Cge
-3x
-3x
+ C3xe
+ C4хе Х сos(2х) + Cзxе X sin(2x) + Cөx?e Х cos(2x) +
Cje* + c2e
-X sin(2x)
(5) у(x)
cos(2x) + с5хе
sin(2x) + cөх*е
C7x?e
c7x²e
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