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Diff EQ question

  • Thread starter kdinser
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  • #1
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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)?
 

Answers and Replies

  • #2
52
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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
 
  • #3
337
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That's what I was hoping for, thanks.
 
  • #4
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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...
 
  • #5
dextercioby
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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.
 

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