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State True or False, no justification needed. (a) The functions f₁ (t) = t and f2(t) = e²t are linearly independent on the interval (-1,1). (b) The functions g₁ (t) = 2 sin² t and g2 (t) = 1 − cos² t are linearly independent on the interval (-1,1).

State True or False, no justification needed. (a) The functions f₁ (t) = t and f2(t) = e²t are linearly independent on the interval (-1,1). (b) The functions g₁ (t) = 2 sin² t and g2 (t) = 1 − cos² t are linearly independent on the interval (-1,1).

Advanced Engineering Mathematics
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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State True or False, no justification needed. (a) The functions f₁ (t) = t and f₂(t) = e²t are linearly independent on the interval (-1,1). (b) The functions g₁ (t) = 2 sin² t and g₂ (t) = 1 − cos² t are linearly independent on the interval (−1,1). (c) The function x(t) = et - e-t is a solution to the equation (d) The function x = x+e-t. y(t) = is a solution to the equation -2 t² +1 y' = ty².
Transcribed Image Text:State True or False, no justification needed. (a) The functions f₁ (t) = t and f₂(t) = e²t are linearly independent on the interval (-1,1). (b) The functions g₁ (t) = 2 sin² t and g₂ (t) = 1 − cos² t are linearly independent on the interval (−1,1). (c) The function x(t) = et - e-t is a solution to the equation (d) The function x = x+e-t. y(t) = is a solution to the equation -2 t² +1 y' = ty².
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