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

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

Consider the linear differential equation $y^{\prime \prime}+4 y^{\prime}+4 y=0$ (a) $e^{-2x}$ is a solution. (b) $xe^{-2x}$ is a solution. (c) $x^2e^{-2x}$ is not a solution. (d) $(x+2)e^{-2x}$ is a solution.