The general solution of the differential equation ` ln ((dy)/(dx))+x =0` is ?

Options

A. ` y = =e^(-x)+c`
B. ` y= -e^(-x) +c`
C. `y = e^(x)+c`
D. `y= -c^(x) =c`

Answer

A

Explanation

Let `ln((dy)/(dx))+x =0 Rightarrow ln((dy)/(dx)) =-x`
` Rightarrow (dy)/(dx) = e^(-x)`
Integrate both the side.
` y= -e^(-x) +c`