Question

The general solution of the differential equation.

Answer 1

\[y'' + 2y'=0\]

Answer 2

we can write this as:
\[(D^2+2D)y=0\\
D(D+2)y=0
\]
where D = differential operator.
this is a homogenous DE
the differential operator has the roots:
0 and -2
so, the general solution is:
\[y(x)=Ae^{0x}+Be^{-2x}\\
y(x)=A+Be^{-2x}
\]

Answer 3

thank you @electrokid