Answer
a) and d)
Work Step by Step
a) $(e^{3x}))''-(e^{3x}))'-6e^{3x}=9e^{3x}-3e^{3x}-6e^{3x}=0$, thus this is a solution.
b) $(e^{2x}))''-(e^{2x}))'-6e^{2x}=4e^{2x}-2e^{2x}-6e^{2x}=-4e^{2x}$, thus this is not a solution.
c) $(e^{-3x}))''-(e^{-3x}))'-6e^{-3x}=9e^{-3x}+3e^{-3x}-6e^{-3x}=6e^{3x}$, thus this is not a solution.
d) $(e^{-2x}))''-(e^{-2x}))'-6e^{-2x}=4e^{-2x}+2e^{-2x}-6e^{-2x}=0$, thus this is a solution.
