# second order differential constant coefficients homogeneous

• Oct 1st 2008, 09:45 AM
andrewsx
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
• Oct 1st 2008, 09:50 AM
Chris L T521
Quote:

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 \$\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