Q8) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant coefficients are 0,0,0,2+5i,2-5i, then the general solutiom of this ODE, is: a) C₁ + ₂x + C3x² + e²x [Acos(x) + Bsin(x)] b) C₁+C₂x + C3x² + esx[Acos (2x) + Bsin(2x)] c) C₁x + ₂x² + c3x³ + e*[Acos (5x) + Bsin(5x)] d) C₁ + C₂x + C3x² + e2x [Acos(5x) + Bsin(5x)]

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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Q8) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant
coefficients are 0,0,0,2+5i,2-5i, then the general solutiom of this ODE, is:
a) C₁ + ₂x + C3x² + e²x [Acos(x) + Bsin(x)]
b) C₁+C₂x + C3x² + esx[Acos (2x) + Bsin(2x)]
c) C₁x + ₂x² + c3x³ + e*[Acos (5x) + Bsin(5x)]
d) C₁ + C₂x + C3x² + e2x [Acos(5x) + Bsin(5x)]
Transcribed Image Text:Q8) Assume that the roots of a characteristic polynomial of a homogeneous ODE with constant coefficients are 0,0,0,2+5i,2-5i, then the general solutiom of this ODE, is: a) C₁ + ₂x + C3x² + e²x [Acos(x) + Bsin(x)] b) C₁+C₂x + C3x² + esx[Acos (2x) + Bsin(2x)] c) C₁x + ₂x² + c3x³ + e*[Acos (5x) + Bsin(5x)] d) C₁ + C₂x + C3x² + e2x [Acos(5x) + Bsin(5x)]
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