Given:
The solution of a differential equation is
[tex]y^{\prime}^{\prime}-y=0[/tex]
Required:
We need to find the differential equation
Explanation:
For option A
[tex]y=e^x[/tex]
put in given
[tex]\begin{gathered} y^{\prime}^{\prime}-y=0 \\ e^x-e^x=0 \end{gathered}[/tex]
option A is possible
For option B
[tex]y=sinx[/tex][tex]y^{\prime}^{\prime}-y=-sinx-sinx=-2sinx[/tex]
not possible
For option C
[tex]y=cos3x[/tex][tex]y^{\prime}^{\prime}-y=-9cos3x-cos3x=-10cos3x[/tex]
not possible
For option D
[tex]y=e^{-2x}[/tex][tex]y^{\prime}^{\prime}-y=4e^{-2x}-e^{-2x}=3e^{-2x}[/tex]
not possible
Final answer:
Option A
