# Diff EQ question

When you are trying to determine the general solution of a homogeneous linear ordinary differential equation, after you find the roots, how do you decide which goes with c1 and which goes with c2?

example:

y''-3y'+2y=0

Factoring the auxiliary equation

m^2-3m+2=0=(m-1)(m-2)

is there some kind of convention as to which gets named as m1 and m2?
It seems like every time I do one of these kinds of problems, my answer is the opposite of the books. Is there any difference between

y=c1e^(x)+c2e^(2x) and y=c1e^(2x)+c2e^(x)?

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c1 and c2 are arbitrary constants which must be determined by initial conditions only. so there is no difference if you interchange them

That's what I was hoping for, thanks.

Is there any difference between

y=c1e^(x)+c2e^(2x) and y=c1e^(2x)+c2e^(x)?
No, they have no different....... you can write it either way.....

is there some kind of convention as to which gets named as m1 and m2?
It depend on the publisher...

dextercioby
Homework Helper
kdinser said:
When you are trying to determine the general solution of a homogeneous linear ordinary differential equation, after you find the roots, how do you decide which goes with c1 and which goes with c2?

example:

y''-3y'+2y=0

Factoring the auxiliary equation

m^2-3m+2=0=(m-1)(m-2)

is there some kind of convention as to which gets named as m1 and m2?
It seems like every time I do one of these kinds of problems, my answer is the opposite of the books. Is there any difference between

y=c1e^(x)+c2e^(2x) and y=c1e^(2x)+c2e^(x)?
Read the result from right to left.I'm sure it will coincide with yours...

Daniel.