`y*(x+1) + y' = 0 , y(-2) = 1` Find the particular solution that satisfies the initial condition

This differential equation may be expressed as

`(y')/y = -x - 1`

and then integrated:

`ln|y| = -x^2/2 - x + C, or y = Ce^(-x^2/2 - x),`

where `C` is any constant.

To determine the specific constant, we use the given condition `y(-2) = 1,` which gives

`1 = C e^(-2 + 2) = C,`

so the final answer is  `y(x) =e^(-x^2/2 - x).`