Chapter 4 - Vector Spaces - 4.8 Applications of Vector Spaces - 4.8 Exercises - Page 219: 12

(a) 3$e^{x^{2}}$ is a solution. (b) $x e^{x^{2}}$ is not a solution. (c) $x^{2} e^{x}$ is not a solution. (d) $x e^{-x}$ is not a solution.

Consider the linear differential equation $y^{\prime}-2 x y=0$ (a) 3$e^{x^{2}}$ is a solution. (b) $x e^{x^{2}}$ is not a solution. (c) $x^{2} e^{x}$ is not a solution. (d) $x e^{-x}$ is not a solution.