Question

# 2⋅(dy/dx)+2y=0

Differential equations
$$\displaystyle{2}⋅{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}+{2}{y}={0}$$

This equation is $$y'+2y=0$$
Its characteristic equation is $$\displaystyle{r}+{2}={0}\to{r}=-{2}$$
Therefore, the solution is $$\displaystyle{y}={C}{e}^{{-{{2}}}}{x}$$