Answer: Testing for Linear Independence In Exercises 3138,

Chapter 4, Problem 36

(choose chapter or problem)

In Exercises 31–38, (a) verify that each solution satisfies the differential equation, (b) test the set of solutions for linear independence, and (c) if the set is linearly independent, then write the general solution of the differential equation.

Differential Equation                                                                         Solutions

\(y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=0\)       \(\left\{e^{-x}, x e^{-x}, x^{2} e^{-x}\right\}\)

Text Transcription:

y^prime prime prime +3y^prime prime +3y^prime +y=0

{e^-x, xe^-x, x^2 e^-x}

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