Answer
(a) $e^{x-x^2}$ is not a solution.
(b) $2e^{x-x^2}$ is not a solution.
(c) $3e^{x-x^2}$ is not a solution.
(d) $4e^{x-x^2}$ is not a solution.
Work Step by Step
Consider the differential equation $y^{\prime}(2 x-1) y=0$
(a) $e^{x-x^2}$ is not a solution.
(b) $2e^{x-x^2}$ is not a solution.
(c) $3e^{x-x^2}$ is not a solution.
(d) $4e^{x-x^2}$ is not a solution.