y₁(t) = et 2e-t and y₂(t) = 2te-t + et are both solutions of nonhomogeneous DE y" + 2y + y = g(t), t> 0. Which one of the statements below is FALSE ? (A) g(t) 4et (B) y(t) = C₁(et 2e-t) + C₂ (2te-t + et) is a general solution of the equation. (C) y(t) = 0 is not a solution of the equation. (D) y(t) = et is another solution of the equation.

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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y₁(t) = et 2e¯t and y₂(t) = 2tet + et are both solutions of nonhomogeneous DE
y" + 2y' + y = g(t), t> 0.
Which one of the statements below is FALSE ?
(A) g(t) = 4et
(B) y(t) = C1₁
(C) y(t)
= = 0
(D) ya (t) = et
(et - 2e-t) +C₂ · (2tet + et) is a general solution of the equation.
.
is not a solution of the equation.
is another solution of the equation.
Transcribed Image Text:y₁(t) = et 2e¯t and y₂(t) = 2tet + et are both solutions of nonhomogeneous DE y" + 2y' + y = g(t), t> 0. Which one of the statements below is FALSE ? (A) g(t) = 4et (B) y(t) = C1₁ (C) y(t) = = 0 (D) ya (t) = et (et - 2e-t) +C₂ · (2tet + et) is a general solution of the equation. . is not a solution of the equation. is another solution of the equation.
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