What is the solution of the differential equation (D³ + 3D² +3D+2) y = 0 ? 0y=Cie O O -2x + C₂e * cos+ C3e-7 sin r 2 3 y = C₁ e 2 +₂ezz C₂e™ 200 y = C₁e-2 + C₂ √³x COS x + Сzez sin sin X 3 2 cosa + С3-² sin COS T x -X Oy=C₁e-2 + C₂e cos √3x + C3e sin √3x V

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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What is the solution of the differential equation
(D³+3D² + 3D + 2) y = 0 ?
Oy=C₁e 2 + C₂e cos+ Ce sin r
= ²
2
Oy=C₁e-2
+ C₂ezz
y = C₁e-2
O y Cie 2
+ C₂e
+ C₂e
COS
√³x + C3e¹² sin
2
√3
2
10
* cos x + C3e sin r
-X
OC
cos √3x + C3e sin √3x
Transcribed Image Text:What is the solution of the differential equation (D³+3D² + 3D + 2) y = 0 ? Oy=C₁e 2 + C₂e cos+ Ce sin r = ² 2 Oy=C₁e-2 + C₂ezz y = C₁e-2 O y Cie 2 + C₂e + C₂e COS √³x + C3e¹² sin 2 √3 2 10 * cos x + C3e sin r -X OC cos √3x + C3e sin √3x
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