yuki
  • yuki
Differential equations
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
give question......
anonymous
  • anonymous
wt of them??
yuki
  • yuki
\[y"+3y'-4y = 0\]

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yuki
  • yuki
if we let \[y= e^{mx}\]
yuki
  • yuki
I know that we can get \[(m^2 +3m-4)e^{mx}=0\]
anonymous
  • anonymous
use characteristic equation: m^2+3m-4=0 m=-4 and m=1 so y=c1e^(-4t)+c2e^t
anonymous
  • anonymous
(d^2+3d-4)y=0 d=4,-1 y=ae^4x+be^-x
yuki
  • yuki
and it factors into \[(m-1)(m+4)=0\]
yuki
  • yuki
so since the roots are real and distinct, y = \[ae^{x}+be^{-4x}\]
anonymous
  • anonymous
CORRECT
anonymous
  • anonymous
it will be ae^4x+be^-x.
yuki
  • yuki
but what if \[y"-10y'+25y = 0 \]
anonymous
  • anonymous
because your char. equation m^2+3m-4=0 has the roots 4,-1.
anonymous
  • anonymous
(a+bx)e^5x
anonymous
  • anonymous
Then you have two same roots m=5 and then y=c1te^5t+c2e^5t
yuki
  • yuki
how do we proceed the problem? do we let \[y= xe^{mx}\]
anonymous
  • anonymous
"because your char. equation m^2+3m-4=0 has the roots 4,-1" dipank this is NOT CORRECT
anonymous
  • anonymous
yes i checked........sorry for that........
anonymous
  • anonymous
noproblem, i just didn't want to confuse..
yuki
  • yuki
for the other root I think there was another way to solve it when the roots are equal and real, the formula was different and I think dipank sounds right but I am not sure how to prove it
anonymous
  • anonymous
long proof..it'd be in your book for sure. circuit theory is the only way i ever wrapped my brain around this concept..a critically damped RLC circuit is modelled by a characteristic equation with two real same roots. Good luck with your proof and further studies though.
dumbcow
  • dumbcow
here is a link that might help you understand repeated roots in characteristic equation http://tutorial.math.lamar.edu/Classes/DE/RepeatedRoots.aspx

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