Chapter 4 - Vector Spaces - 4.8 Applications of Vector Spaces - 4.8 Exercises - Page 219: 7

(a) $\frac{1}{x^2}$ is not a solution. (b) $x^2$ is a solution. (c) $e^{x^2}$ is not a solution. (d) $e^{-x^2}$ is not a solution.

Consider the linear differential equation $x^{2} y^{\prime \prime}-2 y=0$ (a) $\frac{1}{x^2}$ is not a solution. (b) $x^2$ is a solution. (c) $e^{x^2}$ is not a solution. (d) $e^{-x^2}$ is not a solution.