What is the solution of the equation In `((dy)/(dx))+x =0` ?

Options

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

Answer

C

Explanation

Consdier the given differential equation.
In ` ((dy)/(dx))+x=0`
` Rightarrow In ((dy)/(dx))= -x`
` Rightarrow (dy)/(dx) = e^(-x)`
on separating the variables, we get
` dy = e^(-x) dx`
On integrating both sides, we get
` int dy = int e ^(-x) dx`
` Rightarrow y = (e^(-x))/(-1) +C = e^(-x) +C`
` Rightarrow y + e^(-x) = C`