The solution e x , e -x , and e 2x of {d^{3}y}/{dx^{3}}−2 {d^{2}y}/{dx^{2}}−\frac{dy}{dx} + 2y = 0 will be:

Correct Answer is : linearly independent on every real interval.

linearly dependent for xϵ[-2, 2] and linearly independent elsewhere.

linearly independent for xϵ[-1, 1] and linearly independent elsewhere.

linearly independent on every real interval.

linearly dependent for all real x.

AAI ATC Junior Executive 2018 Shift 1 Paper

Question : 100 of 120

Marks: +1, -0

The solution e^x, e^-x, and e^2x of

\;{d^{3}y}/{dx^{3}}−2\;{d^{2}y}/{dx^{2}}−\;{dy}/{dx} + 2y = 0

will be:

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