Differential Equations question Say I was looking for a gene

Differential Equations question:

Say I was looking for a general solution given a higher order differential equation. Let\'s use y\'\'\'-5y\'\'+3y\'+9=0.

I rewrite is as m³-5m²+3m+9=0 and factored it as (m-3)²(m+1)=0. Does it matter if write the general solution as

y=C₁e^3x+C₂xe^3x+C₃e^-x or  y=C₁e^-x+C₂e^3x+C₃xe^3x

Basically, are the C\'s interchangeable?

Solution

As c are just a constant they are interchangable there will be no effect on solution.