Show that y, (x) = e 3* and y,(x) = e 4x are linearly independent on I = (-0, ∞) and find a second order homogeneous equation having the pair as a fundemental set of solutions. y" -y'+12y =0 b) О у" +3у' — 4у-0 c) O y" - 8y ' +4y=0 d) Оу" +4y'- 12 у -0 y" -y'- 12y=0 f) O None of the above.

Show that y, (x) = e 3* and y,(x) = e 4x are linearly independent on I = (-0, ∞) and find a second order homogeneous equation having the pair as a fundemental set of solutions. y" -y'+12y =0 b) О у" +3у' — 4у-0 c) O y" - 8y ' +4y=0 d) Оу" +4y'- 12 у -0 y" -y'- 12y=0 f) O None of the above.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 69EQ: Let x=x(t) be a twice-differentiable function and consider the second order differential equation...

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