# Thread: second order differential constant coefficients homogeneous

1. ## second order differential constant coefficients homogeneous

Hello

I got the Roots R=5,2 for y''-7y'+10y=0

So the equation would be y=C1e^5x +C2e^2x

and not y=C1e^2x+C2e^5x OR Does It even matter where you stick the roots????

THanks

2. Originally Posted by andrewsx
Hello

I got the Roots R=5,2 for y''-7y'+10y=0

So the equation would be y=C1e^5x +C2e^2x

and not y=C1e^2x+C2e^5x OR Does It even matter where you stick the roots????

THanks
The order of the coefficients doesn't matter.

You can try it out both ways and see that you'll get the same thing if it was $y_p=C_1e^{2x}+C_2e^{5x}$ or $y_p=C_1e^{5x}+C_2e^{2x}$

However, note that $C_1$ and $C_2$ values you will get from solving it both ways will be different, but you will see that they correspond to the same $e$ term.

--Chris