Is this equation homogenous or inhomogeous?

Question

I have the following differential equation in my perturbation theory notes

$y'' + 2y' = -2y$

$y(0) = 0$

It says in the following section that this equation is inhomogeneous. But I thought equations are inhomogenous if they are of the form

$ay'' + by' + cy = F(x)$ with $F(x) \ne 0$

So why is the above equation described as inhomogeneous? Is it a mistake..or is it something to do with a boundary condition being specified..or is it something else?

Answer 1

your first equation $y''+2y'+2y=0$ is homogeneous and has the solution $y \left( x \right) ={\it \_C1}\,{{\rm e}^{-x}}\sin \left( x \right) +{ \it \_C2}\,{{\rm e}^{-x}}\cos \left( x \right) $