(D) e(-1-v2)x + cze(-1+v2)x If r2+2r-1 = 0 is the characteristic equation of a homogeneous D.E. with constant coefficients, then we can write the general solution as y(x) = %3D (A) C1+ C2x (B) c1 + c2 In x (C) Cie + c2xe" (E) Cie + C2xe¯*

(D) e(-1-v2)x + cze(-1+v2)x If r2+2r-1 = 0 is the characteristic equation of a homogeneous D.E. with constant coefficients, then we can write the general solution as y(x) = %3D (A) C1+ C2x (B) c1 + c2 In x (C) Cie + c2xe" (E) Cie + C2xe¯*

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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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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If r2+2r-1= 0 is the characteristic equation
of a homogeneous D.E. with constant coefficients,
then we can write the general solution as y(x) =
(A) c1+ C2æ
(B) c1 + c2 ln a
(C) ce + cxe"
(D) cje-1-v2)x + crel-1+v2)x
(E) Cie + C2xe

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