Exercise 1.1.12 ( )

$0^{\prime }=2\times 0$ so $y_1(t)=0$ is a solution. $2t={(t^2)}^{\prime }\ne 2(t^2)=2t^2$ so $y_2(t)=t^2$ is not a solution. $6e^{2t}={(3e^{2t})}^{\prime }=2(3e^{2t})=6e^{2t}$ so $y_3(t)=3e^{2t}$ is a solution. $6e^{3t}={(2e^{3t})}^{\prime }\ne 2(2e^{3t})=4^{3t}$ so $y_3(t)=2e^{3t}$ is not a solution.