Question

Which functions are solutions to the differential equation ′′ − = 0? Choose all that apply and justify your answers.

Answer 1

Given:

The solution of a differential equation is

`y^(\prime)^(\prime)-y=0`

Required:

We need to find the differential equation

Step-by-step explanation:

For option A

`y=e^x`

put in given

`\begin{gathered} y^(\prime)^(\prime)-y=0 \\ e^x-e^x=0 \end{gathered}`

option A is possible

For option B

`y=sinx`
`y^(\prime)^(\prime)-y=-sinx-sinx=-2sinx`

not possible

For option C

`y=cos3x`
`y^(\prime)^(\prime)-y=-9cos3x-cos3x=-10cos3x`

not possible

For option D

`y=e^(-2x)`
`y^(\prime)^(\prime)-y=4e^(-2x)-e^(-2x)=3e^(-2x)`

not possible

Final answer:

Option A