Chapter 4 - Vector Spaces - 4.8 Applications of Vector Spaces - 4.8 Exercises - Page 219: 11

(a) ${x}e^{2x}$ is not a solution. (b) $2 e^{2x}$ is a solution. (c) $2 e^{-2x}$ is not a solution. (d) $x e^{-x}$ is not a solution.

Consider the linear differential equation $y^{\prime \prime}-y^{\prime}-2 y=0$ (a) ${x}e^{2x}$ is not a solution. (b) $2 e^{2x}$ is a solution. (c) $2 e^{-2x}$ is not a solution. (d) $x e^{-x}$ is not a solution.