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

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- Oct 1st 2008, 09:45 AMandrewsxsecond 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 - Oct 1st 2008, 09:50 AMChris L T521
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 $\displaystyle y_p=C_1e^{2x}+C_2e^{5x}$ or $\displaystyle y_p=C_1e^{5x}+C_2e^{2x}$

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

--Chris