Question

A solution of y' = -y is the function y(x)= . . .

Answer 1

`y(x)=Ce^(-x)`

Explanation:

We are given that y'=-y

We have to find the solution of given differential equation

`(dy)/(dx)=-y`

`(dy)/(y)=-dx`

Integrating on both sides then we get

`lny=-x+c`

`if\;lna=b` then
`a=e^b`

`y=e^(-x+c)=e^(-x)\cdot e^c`

`y=Ce^(-x)` because
`e^c=Constant=C`

Hence,
`y(x)=Ce^(-x)` is the solution of given differential equation y'=-y