Answer:
[tex]y(x)=Ce^{-x}[/tex]
Step-by-step explanation:
We are given that y'=-y
We have to find the solution of given differential equation
[tex]\frac{dy}{dx}=-y[/tex]
[tex]\frac{dy}{y}=-dx[/tex]
Integrating on both sides then we get
[tex]lny=-x+c[/tex]
[tex]if\;lna=b [/tex] then [tex] a=e^b[/tex]
[tex]y=e^{-x+c}=e^{-x}\cdot e^c[/tex]
[tex]y=Ce^{-x}[/tex] because [tex]e^c=Constant=C[/tex]
Hence,[tex]y(x)=Ce^{-x}[/tex] is the solution of given differential equation y'=-y
