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A third order linear, homogeneous DE whose general solution is y(t) = C₁e-t + C₂e + C3e²t is: [Hint: The general solution implies that r=-1,1 and 2 are the roots of the characteristi equation. Hence r+1, r-1 and r-2 are the factors of the characteristic equation.] O A.y"" - 2y"+y' + 2y = 0 O B. y" + 2y"+y' + 2y = 0 Ocy" - 2y" - y' + 2y = 0 O D. none of these OE.y"" + 2y" - y' + 2y = 0

A third order linear, homogeneous DE whose general solution is y(t) = C₁e-t + C₂e + C3e²t is: [Hint: The general solution implies that r=-1,1 and 2 are the roots of the characteristi equation. Hence r+1, r-1 and r-2 are the factors of the characteristic equation.] O A.y"" - 2y"+y' + 2y = 0 O B. y" + 2y"+y' + 2y = 0 Ocy" - 2y" - y' + 2y = 0 O D. none of these OE.y"" + 2y" - y' + 2y = 0

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...
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A third order linear, homogeneous DE whose general solution is y(t) = C₁e-t + C₂et + C3e²t is: [Hint: The general solution implies that r=-1,1 and 2 are the roots of the characteristi equation. Hence r+1, r-1 and r-2 are the factors of the characteristic equation.] OA.y" - 2y"+y' + 2y = 0 OB. y' + 2y"+y' + 2y = 0 Ocy" - 2y" - y' + 2y = 0 OD. none of these O E. y' + 2y" - y' + 2y = 0
Transcribed Image Text:A third order linear, homogeneous DE whose general solution is y(t) = C₁e-t + C₂et + C3e²t is: [Hint: The general solution implies that r=-1,1 and 2 are the roots of the characteristi equation. Hence r+1, r-1 and r-2 are the factors of the characteristic equation.] OA.y" - 2y"+y' + 2y = 0 OB. y' + 2y"+y' + 2y = 0 Ocy" - 2y" - y' + 2y = 0 OD. none of these O E. y' + 2y" - y' + 2y = 0
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